Pub Date : 2020-12-14DOI: 10.30538/PSRP-OMA2020.0072
E. A. M. A, Hamdallah, E. M. A, Ebead, H. R
In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.
{"title":"On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions","authors":"E. A. M. A, Hamdallah, E. M. A, Ebead, H. R","doi":"10.30538/PSRP-OMA2020.0072","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2020.0072","url":null,"abstract":"In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48481389","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 : 2020-10-30DOI: 10.30538/psrp-oma2021.0088
C. Holliman, L. Hyslop
The Cauchy problem for a higher order modification of the nonlinear Schrödinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent (s > frac{1}{4}). This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. The contraction is proved by using microlocal analysis and a trilinear estimate that is shown via the ([k; Z])-multiplier norm method developed by Terence Tao.
{"title":"Well-posedness for a modified nonlinear Schrödinger equation modeling the formation of rogue waves","authors":"C. Holliman, L. Hyslop","doi":"10.30538/psrp-oma2021.0088","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0088","url":null,"abstract":"The Cauchy problem for a higher order modification of the nonlinear Schrödinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent (s > frac{1}{4}). This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. The contraction is proved by using microlocal analysis and a trilinear estimate that is shown via the ([k; Z])-multiplier norm method developed by Terence Tao.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47188887","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0035
Emmanuel W. Okereke
In this paper, we study a new distribution called the exponentiated transmuted Lindley distribution. The proposed distribution has three special cases namely Lindley, exponentiated Lindley and transmuted Lindley distributions. Along with the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution are discussed. Two applications of the distribution are also part of this article.
{"title":"Exponentiated transmuted lindley distribution with applications","authors":"Emmanuel W. Okereke","doi":"10.30538/PSRP-OMA2019.0035","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0035","url":null,"abstract":"In this paper, we study a new distribution called the exponentiated transmuted Lindley distribution. The proposed distribution has three special cases namely Lindley, exponentiated Lindley and transmuted Lindley distributions. Along with the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution are discussed. Two applications of the distribution are also part of this article.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47775638","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0028
A. C. Cavalheiro
Ω⊂RN is a bounded open set, f ω2 ∈Lp (Ω, ω2), G ν2 ∈ [Ls (Ω, ν2)] , ω1, ω2, ν1 and ν2 are four weight functions (i.e., ωi and νi, i = 1, 2 are locally integrable functions on RN such that 0 < ωi(x), νi(x) < ∞ a.e. x∈RN), ∆ is the Laplacian operator, 1 < q, s < p < ∞, 1/p + 1/p ′ = 1 and 1/s + 1/s ′ = 1. For degenerate partial differential equations, i.e., equations with various types of singularities in the coefficients, it is natural to look for solutions in weighted Sobolev spaces (see [1–8]). The type of a weight depends on the equation type. A class of weights, which is particularly well understood, is the class of Ap weights that was introduced by B.Muckenhoupt in the early 1970’s (see [7]). These classes have found many useful applications in harmonic analysis (see [9] and [10]). Another reason for studying Ap-weights is the fact that powers of the distance to submanifolds of RN often belong to Ap (see [8] and [11]). There are, in fact, many interesting examples of weights (see [6] for p-admissible weights). In the non-degenerate case (i.e. with ω(x) ≡ 1), for all f ∈ Lp(Ω) the Poisson equation associated with the Dirichlet problem { −∆u = f (x), in Ω u(x) = 0, in ∂Ω
{"title":"Existence and uniqueness results for Navier problems with degenerated operators","authors":"A. C. Cavalheiro","doi":"10.30538/PSRP-OMA2019.0028","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0028","url":null,"abstract":"Ω⊂RN is a bounded open set, f ω2 ∈Lp (Ω, ω2), G ν2 ∈ [Ls (Ω, ν2)] , ω1, ω2, ν1 and ν2 are four weight functions (i.e., ωi and νi, i = 1, 2 are locally integrable functions on RN such that 0 < ωi(x), νi(x) < ∞ a.e. x∈RN), ∆ is the Laplacian operator, 1 < q, s < p < ∞, 1/p + 1/p ′ = 1 and 1/s + 1/s ′ = 1. For degenerate partial differential equations, i.e., equations with various types of singularities in the coefficients, it is natural to look for solutions in weighted Sobolev spaces (see [1–8]). The type of a weight depends on the equation type. A class of weights, which is particularly well understood, is the class of Ap weights that was introduced by B.Muckenhoupt in the early 1970’s (see [7]). These classes have found many useful applications in harmonic analysis (see [9] and [10]). Another reason for studying Ap-weights is the fact that powers of the distance to submanifolds of RN often belong to Ap (see [8] and [11]). There are, in fact, many interesting examples of weights (see [6] for p-admissible weights). In the non-degenerate case (i.e. with ω(x) ≡ 1), for all f ∈ Lp(Ω) the Poisson equation associated with the Dirichlet problem { −∆u = f (x), in Ω u(x) = 0, in ∂Ω","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44450552","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0033
A. Ardjouni, A. Djoudi
{"title":"Positive solutions for nonlinear Caputo-Hadamard fractional differential equations with integral boundary conditions","authors":"A. Ardjouni, A. Djoudi","doi":"10.30538/PSRP-OMA2019.0033","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0033","url":null,"abstract":"","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46651988","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0030
H. Essaouini, Fs, Morocco. Tetuan, P. Capodanno
Abstract: In this paper, we study the small oscillations of a visco-elastic fluid that is heated from below and fills completely a rigid container, restricting to the more simple Oldroyd model. We obtain the operatorial equations of the problem by using the Boussinesq hypothesis. We show the existence of the spectrum, prove the stability of the system if the kinematic coefficient of viscosity and the coefficient of temperature conductivity are sufficiently large and the existence of a set of positive real eigenvalues having a point of the real axis as point of accumulation. Then, we prove that the problem can be reduced to the study of a Krein-Langer pencil and obtain new results concerning the spectrum. Finally, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of the semigroups theory.
{"title":"Small convective motions of a visco-elastic fluid filling completely a container when the fluid is heated from below","authors":"H. Essaouini, Fs, Morocco. Tetuan, P. Capodanno","doi":"10.30538/PSRP-OMA2019.0030","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0030","url":null,"abstract":"Abstract: In this paper, we study the small oscillations of a visco-elastic fluid that is heated from below and fills completely a rigid container, restricting to the more simple Oldroyd model. We obtain the operatorial equations of the problem by using the Boussinesq hypothesis. We show the existence of the spectrum, prove the stability of the system if the kinematic coefficient of viscosity and the coefficient of temperature conductivity are sufficiently large and the existence of a set of positive real eigenvalues having a point of the real axis as point of accumulation. Then, we prove that the problem can be reduced to the study of a Krein-Langer pencil and obtain new results concerning the spectrum. Finally, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of the semigroups theory.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69237991","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0040
Mohamed Toumlilin
In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data u0 belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.
{"title":"Global well-posedness and analyticity for generalized porous medium equation in critical Fourier-Besov-Morrey spaces","authors":"Mohamed Toumlilin","doi":"10.30538/psrp-oma2019.0040","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0040","url":null,"abstract":"In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data u0 belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41558593","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0039
Abdelmajid Ali Dafallah, Qiaozhen Ma, Ahmed Eshag Mohamed
Abstract: In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on Rn. Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.
{"title":"Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise","authors":"Abdelmajid Ali Dafallah, Qiaozhen Ma, Ahmed Eshag Mohamed","doi":"10.30538/psrp-oma2019.0039","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0039","url":null,"abstract":"Abstract: In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on Rn. Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43360198","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0027
Afshan Perveen, Samina Kausar, W. Nazeer
In this paper, we present a new non-convex hybrid iteration algorithm for common fixed points of a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in the domains of Hilbert spaces.
{"title":"Strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces","authors":"Afshan Perveen, Samina Kausar, W. Nazeer","doi":"10.30538/PSRP-OMA2019.0027","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0027","url":null,"abstract":"In this paper, we present a new non-convex hybrid iteration algorithm for common fixed points of a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in the domains of Hilbert spaces.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41929565","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0032
M. Almatrafi
It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations: xn+1 = xn−1yn−3 yn−1 (−1− xn−1yn−3) , yn+1 = yn−1xn−3 xn−1 (±1± yn−1xn−3) , n = 0, 1, ..., where the initial data x−3, x−2, x−1, x0, y−3, y−2, y−1 and y0 are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.
{"title":"Solutions structures for some systems of fractional difference equations","authors":"M. Almatrafi","doi":"10.30538/PSRP-OMA2019.0032","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0032","url":null,"abstract":"It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations: xn+1 = xn−1yn−3 yn−1 (−1− xn−1yn−3) , yn+1 = yn−1xn−3 xn−1 (±1± yn−1xn−3) , n = 0, 1, ..., where the initial data x−3, x−2, x−1, x0, y−3, y−2, y−1 and y0 are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48604420","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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