Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.07
P. Pucci
"This paper is devoted to a subject that Professor Csaba Varga suggested during his frequent visits to the University of Perugia and in my regular stays at the ""Babe s-Bolyai"" University. More speci cally, continuing the work started in [7] jointly with Professor Varga, here we establish the existence of two nontrivial (weak) solutions of some one parameter eigenvalue (p,q)-Laplacian problems under homogeneous Dirichlet boundary conditions in bounded domains of R^N."
{"title":"Multiple solutions for eigenvalue problems involving the (p,q)-Laplacian","authors":"P. Pucci","doi":"10.24193/subbmath.2023.1.07","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.07","url":null,"abstract":"\"This paper is devoted to a subject that Professor Csaba Varga suggested during his frequent visits to the University of Perugia and in my regular stays at the \"\"Babe s-Bolyai\"\" University. More speci cally, continuing the work started in [7] jointly with Professor Varga, here we establish the existence of two nontrivial (weak) solutions of some one parameter eigenvalue (p,q)-Laplacian problems under homogeneous Dirichlet boundary conditions in bounded domains of R^N.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88119845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.10
Csaba Farkas, I. Mezei, Zsuzsanna-Timea Nagy
"Let $(M,g)$ be a Cartan-Hadamard manifold. For certain positive numbers $mu$ and $lambda$, we establish the multiplicity of solutions to the problem $$Delta_g^2 u-Delta_g u+u=mu frac{u}{d_g(x_0,x)^4}+lambda alpha(x)f(u), mbox{ in } M,$$ where $x_0in M$, while $f:RtoR$ is continuous function, superlinear at zero and sublinear at infinity."
{"title":"Multiple solution for a fourth-order nonlinear eigenvalue problem with singular and sublinear potential","authors":"Csaba Farkas, I. Mezei, Zsuzsanna-Timea Nagy","doi":"10.24193/subbmath.2023.1.10","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.10","url":null,"abstract":"\"Let $(M,g)$ be a Cartan-Hadamard manifold. For certain positive numbers $mu$ and $lambda$, we establish the multiplicity of solutions to the problem $$Delta_g^2 u-Delta_g u+u=mu frac{u}{d_g(x_0,x)^4}+lambda alpha(x)f(u), mbox{ in } M,$$ where $x_0in M$, while $f:RtoR$ is continuous function, superlinear at zero and sublinear at infinity.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"177 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74942858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.08
M. Mihăilescu, Denisa Stancu-Dumitru
"The goal of this paper is to collect some known results on the monotonicity with respect to $p$ of the best constants associated with Sobolev immersions of type $W_0^{1,p}(Omega)hookrightarrow L^q(Omega)$ when $qin{1,p,infty}$. More precisely, letting $$lambda(p,q;Omega):=inflimits_{uin W_0^{1,p}(Omega) setminus{0}}{|;|nabla u|_D;|_{L^p(Omega)}}{|u|_{L^q(Omega)}^{-1}},,$$ we recall some monotonicity results related with the following functions begin{eqnarray*} (1,infty)ni p&mapsto &|Omega|^{p-1}lambda(p,1;Omega)^p,, (1,infty)ni p&mapsto &lambda(p,p;Omega)^p,, (D,infty)ni p&mapsto &lambda(p,infty;Omega)^p,, end{eqnarray*} when $Omegasubset mathbb{R}^{D}$ is a given open, bounded and convex set with smooth boundary."
{"title":"\"Monotonicity with respect to p of the best constants associated with Sobolev immersions of type $W_0^{1,p}(Omega)hookrightarrow L^q(Omega)$ when $qin{1,p,infty}$\"","authors":"M. Mihăilescu, Denisa Stancu-Dumitru","doi":"10.24193/subbmath.2023.1.08","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.08","url":null,"abstract":"\"The goal of this paper is to collect some known results on the monotonicity with respect to $p$ of the best constants associated with Sobolev immersions of type $W_0^{1,p}(Omega)hookrightarrow L^q(Omega)$ when $qin{1,p,infty}$. More precisely, letting $$lambda(p,q;Omega):=inflimits_{uin W_0^{1,p}(Omega) setminus{0}}{|;|nabla u|_D;|_{L^p(Omega)}}{|u|_{L^q(Omega)}^{-1}},,$$ we recall some monotonicity results related with the following functions begin{eqnarray*} (1,infty)ni p&mapsto &|Omega|^{p-1}lambda(p,1;Omega)^p,, (1,infty)ni p&mapsto &lambda(p,p;Omega)^p,, (D,infty)ni p&mapsto &lambda(p,infty;Omega)^p,, end{eqnarray*} when $Omegasubset mathbb{R}^{D}$ is a given open, bounded and convex set with smooth boundary.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77162879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.03
Francesca Farraci
"In the present note we study a semilinear elliptic Dirichlet problem involving a singular term with variable exponent of the following type $$left{ begin{array}{ll} -Delta u= frac{f(x)}{u^{gamma(x)} }, & hbox{ in } Omega u>0, & hbox{ in } Omega u=0, & hbox{on } partial Omega end{array} right.eqno{(mathcal{P})}$$ Existence and uniqueness results are proved when $fgeq 0$."
{"title":"On a singular elliptic problem with variable exponent","authors":"Francesca Farraci","doi":"10.24193/subbmath.2023.1.03","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.03","url":null,"abstract":"\"In the present note we study a semilinear elliptic Dirichlet problem involving a singular term with variable exponent of the following type $$left{ begin{array}{ll} -Delta u= frac{f(x)}{u^{gamma(x)} }, & hbox{ in } Omega u>0, & hbox{ in } Omega u=0, & hbox{on } partial Omega end{array} right.eqno{(mathcal{P})}$$ Existence and uniqueness results are proved when $fgeq 0$.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"2005 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83015786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.04
Nicuşor Costea, Shengda Zeng
"In this paper we consider a class of double phase differential inclusions of the type $$left{ begin{array}{ll} -{rm div;}left(|nabla u|^{p-2}nabla u+mu(x)|nabla u|^{q-2}nabla uright) in partial_C^2 f(x,u) , & mbox{ in }Omega, u=0, & mbox{ on }partialOmega, end{array} right.$$ where $Omega subset mathbb{R}^N$, with $Nge 2$, is a bounded domain with Lipschitz boundary, $f(x,t)$ is measurable w.r.t. the first variable on $Omega$ and locally Lipschitz w.r.t. the second variable and $partial_C^2 f(x,cdot)$ stands for the Clarke subdifferential of $tmapsto f(x,t)$. The variational formulation of the problem gives rise to a so-called hemivariational inequality and the corresponding energy functional is not differentiable, but only locally Lipschitz. We use nonsmooth critical point theory to prove the existence of at least one weak solution, provided the $partial_C^2 f(x,cdot)$ satisfies an appropriate growth condition."
{"title":"Existence results for Dirichlet double phase differential inclusions","authors":"Nicuşor Costea, Shengda Zeng","doi":"10.24193/subbmath.2023.1.04","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.04","url":null,"abstract":"\"In this paper we consider a class of double phase differential inclusions of the type $$left{ begin{array}{ll} -{rm div;}left(|nabla u|^{p-2}nabla u+mu(x)|nabla u|^{q-2}nabla uright) in partial_C^2 f(x,u) , & mbox{ in }Omega, u=0, & mbox{ on }partialOmega, end{array} right.$$ where $Omega subset mathbb{R}^N$, with $Nge 2$, is a bounded domain with Lipschitz boundary, $f(x,t)$ is measurable w.r.t. the first variable on $Omega$ and locally Lipschitz w.r.t. the second variable and $partial_C^2 f(x,cdot)$ stands for the Clarke subdifferential of $tmapsto f(x,t)$. The variational formulation of the problem gives rise to a so-called hemivariational inequality and the corresponding energy functional is not differentiable, but only locally Lipschitz. We use nonsmooth critical point theory to prove the existence of at least one weak solution, provided the $partial_C^2 f(x,cdot)$ satisfies an appropriate growth condition.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76205282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-17DOI: 10.24193/subbmath.2023.1.15
"In this work we construct the deficient quartic spline with the knots following the Marsden's scheme and prove the existence and uniqueness of the deficient quartic spline with minimal deviation by the data polygon. The inter- polation error estimate of the obtained quartic spline is given in terms of the modulus of continuity. A numerical example is included in order to illustrate the geometrical behaviour of the quartic spline with minimal quadratic oscillation in average in comparison with the two times continuous di erentiable de cient quartic spline."
{"title":"Deficient quartic spline of Marsden type with minimal deviation by the data polygon","authors":"","doi":"10.24193/subbmath.2023.1.15","DOIUrl":"https://doi.org/10.24193/subbmath.2023.1.15","url":null,"abstract":"\"In this work we construct the deficient quartic spline with the knots following the Marsden's scheme and prove the existence and uniqueness of the deficient quartic spline with minimal deviation by the data polygon. The inter- polation error estimate of the obtained quartic spline is given in terms of the modulus of continuity. A numerical example is included in order to illustrate the geometrical behaviour of the quartic spline with minimal quadratic oscillation in average in comparison with the two times continuous di erentiable de cient quartic spline.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84525401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.24193/subbmath.2022.4.06
M. Jafari, Ahmad Motamednezad, E. A. Adegani
"In this paper, we investigate bounds of the coefficients for subclass of analytic and bi-univalent functions. The results presented in this paper would generalize and improve some recent works and other authors."
{"title":"Coefficient estimates for a subclass of analytic functions by Srivastava-Attiya operator","authors":"M. Jafari, Ahmad Motamednezad, E. A. Adegani","doi":"10.24193/subbmath.2022.4.06","DOIUrl":"https://doi.org/10.24193/subbmath.2022.4.06","url":null,"abstract":"\"In this paper, we investigate bounds of the coefficients for subclass of analytic and bi-univalent functions. The results presented in this paper would generalize and improve some recent works and other authors.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73413497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.2478/subboec-2022-0014
Emmanuel Oloke, W. Olanipekun, O. Mabinuori, Lucas B. Ojo, T. Aderemi
Abstract The critical need to create economic prosperity and ensure inclusive and equitable education and lifelong learning for all, especially in developing countries has been the motivation behind the various advocacies by the policymakers and other stakeholders in these countries to achieve the SDGs comes 2030. Meanwhile, ECOWAS sub region is characterized with the lowest human capital development alongside the highest rates of illiteracy in the world despite the continuous rise in government educational spending over the years. Against this backdrop, the role of government educational spending on human capital development in ECOWAS sub-region has been investigated with a view to driving one of the strategic goals of Sustainable Development- inclusive and equitable education and lifelong learning for all. In order to achieve this, annual data from 1990 to 2019 was utilized using a panel ARDL as a technique of estimation. The findings that emerged in this work are summarized as follows; the relationship between government educational spending and human capital development in ECOWAS sub region is more of a long run phenomenon. Therefore, government educational spending and human capital development have a positive and significant relationship in the long run. In the light of the above findings, this study therefore makes the following recommendations for the policymakers in ECOWAS sub region and by extension developing countries, any time the goal of these policymakers is inclusive and equitable lifelong learning via human capital development, the government at levels should embark on sustainable educational spending. In the same vein, these policymakers should be committed to funding of educational sector as stipulated by both the United Nations and the Abuja declaration of 2001, advocating for 26% of annual budget for educational sector in developing countries.
{"title":"Government Educational Spending and Human Capital Development in ECOWAS Sub-Region: Implication For Sustainable Development","authors":"Emmanuel Oloke, W. Olanipekun, O. Mabinuori, Lucas B. Ojo, T. Aderemi","doi":"10.2478/subboec-2022-0014","DOIUrl":"https://doi.org/10.2478/subboec-2022-0014","url":null,"abstract":"Abstract The critical need to create economic prosperity and ensure inclusive and equitable education and lifelong learning for all, especially in developing countries has been the motivation behind the various advocacies by the policymakers and other stakeholders in these countries to achieve the SDGs comes 2030. Meanwhile, ECOWAS sub region is characterized with the lowest human capital development alongside the highest rates of illiteracy in the world despite the continuous rise in government educational spending over the years. Against this backdrop, the role of government educational spending on human capital development in ECOWAS sub-region has been investigated with a view to driving one of the strategic goals of Sustainable Development- inclusive and equitable education and lifelong learning for all. In order to achieve this, annual data from 1990 to 2019 was utilized using a panel ARDL as a technique of estimation. The findings that emerged in this work are summarized as follows; the relationship between government educational spending and human capital development in ECOWAS sub region is more of a long run phenomenon. Therefore, government educational spending and human capital development have a positive and significant relationship in the long run. In the light of the above findings, this study therefore makes the following recommendations for the policymakers in ECOWAS sub region and by extension developing countries, any time the goal of these policymakers is inclusive and equitable lifelong learning via human capital development, the government at levels should embark on sustainable educational spending. In the same vein, these policymakers should be committed to funding of educational sector as stipulated by both the United Nations and the Abuja declaration of 2001, advocating for 26% of annual budget for educational sector in developing countries.","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"5 1","pages":"37 - 52"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73614227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.24193/subbmath.2022.4.14
Khelladi Samia, Benterki Djamel
"In this paper, we present some hybrid methods for solving unconstrained optimization problems. These methods are defined using proper combinations of the search directions and included parameters in conjugate gradient and quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno (CG-BFGS). Their global convergence under the Wolfe line search is analyzed for general objective functions. Numerical experiments show the superiority of the modified hybrid (CG-BFGS) method with respect to some existing methods."
{"title":"Hybrid conjugate gradient-BFGS methods based on Wolfe line search","authors":"Khelladi Samia, Benterki Djamel","doi":"10.24193/subbmath.2022.4.14","DOIUrl":"https://doi.org/10.24193/subbmath.2022.4.14","url":null,"abstract":"\"In this paper, we present some hybrid methods for solving unconstrained optimization problems. These methods are defined using proper combinations of the search directions and included parameters in conjugate gradient and quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno (CG-BFGS). Their global convergence under the Wolfe line search is analyzed for general objective functions. Numerical experiments show the superiority of the modified hybrid (CG-BFGS) method with respect to some existing methods.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75857657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.24193/subbmath.2022.4.09
M. Kerker
"In this paper we consider a class of quasilinear wave equations $$u_{tt}-Delta_{alpha} u-omega_1Delta u_t-omega_2Delta_{beta}u_t+muvert u_tvert^{m-2}u_t=vert uvert^{p-2}u,$$ associated with initial and Dirichlet boundary conditions. Under certain conditions on $alpha,beta,m,p$, we show that any solution with positive initial energy, blows up in finite time. Furthermore, a lower bound for the blow-up time will be given."
{"title":"Finite time blow-up for quasilinear wave equations with nonlinear dissipation","authors":"M. Kerker","doi":"10.24193/subbmath.2022.4.09","DOIUrl":"https://doi.org/10.24193/subbmath.2022.4.09","url":null,"abstract":"\"In this paper we consider a class of quasilinear wave equations $$u_{tt}-Delta_{alpha} u-omega_1Delta u_t-omega_2Delta_{beta}u_t+muvert u_tvert^{m-2}u_t=vert uvert^{p-2}u,$$ associated with initial and Dirichlet boundary conditions. Under certain conditions on $alpha,beta,m,p$, we show that any solution with positive initial energy, blows up in finite time. Furthermore, a lower bound for the blow-up time will be given.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84264027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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