We expand the HANDY (Human And Nature DYnamics) model for the socioeconomic dynamics of a large stratified society. The basic model was introduced in Motesharrei (Dissertation 2014) and Motesharrei et al. (2016). It is a nonlinear system of ODEs for a `simple society' of Elites, Workers, Wealth, and Natural Resources. Following Ali Kadhim (Dissertation 2021), we add social mobility between the classes and split natural resources into renewables and nonrenewables. We establish the existence, boundedness and positivity of the solutions, and investigates the stability of the steady states. The model admits stable steady states, and there is numerical evidence of stable periodic solutions and limit cycles. Simulations depict the different qualitative types of model behavior: convergence to steady states, periodic oscillations, collapse.
For more information see https://ejde.math.txstate.edu/Volumes/2023/59/abstr.html
我们将HANDY(人类与自然动力学)模型扩展为一个大型分层社会的社会经济动态。Motesharrei (Dissertation 2014)和Motesharrei et al.(2016)介绍了基本模型。这是一个由精英、工人、财富和自然资源组成的“简单社会”的非线性ode系统。继Ali Kadhim(论文2021)之后，我们增加了阶级之间的社会流动性，并将自然资源分为可再生能源和不可再生能源。我们建立了解的存在性、有界性和正性，并研究了稳态的稳定性。该模型承认稳定的稳态，并有稳定周期解和极限环的数值证据。模拟描述了不同定性类型的模型行为:收敛到稳态，周期振荡，崩溃。
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{"title":"Analysis and simulations of the HANDY model with social mobility, renewables and nonrenewables","authors":"Meir Shillor, Thanaa Ali Kadhim","doi":"10.58997/ejde.2023.59","DOIUrl":"https://doi.org/10.58997/ejde.2023.59","url":null,"abstract":"We expand the HANDY (Human And Nature DYnamics) model for the socioeconomic dynamics of a large stratified society. The basic model was introduced in Motesharrei (Dissertation 2014) and Motesharrei et al. (2016). It is a nonlinear system of ODEs for a `simple society' of Elites, Workers, Wealth, and Natural Resources. Following Ali Kadhim (Dissertation 2021), we add social mobility between the classes and split natural resources into renewables and nonrenewables. We establish the existence, boundedness and positivity of the solutions, and investigates the stability of the steady states. The model admits stable steady states, and there is numerical evidence of stable periodic solutions and limit cycles. Simulations depict the different qualitative types of model behavior: convergence to steady states, periodic oscillations, collapse.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/59/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a perforated domain (Omega(epsilon)) of (mathbb{R}^2) with a small hole of size (epsilon) and we study the behavior of the solution of a mixed Neumann-Robin problem in (Omega(epsilon)) as the size (epsilon) of the small hole tends to (0). In addition to the geometric degeneracy of the problem, the nonlinear (epsilon)-dependent Robin condition may degenerate into a Neumann condition for (epsilon=0) and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as (epsilon) tends to (0) and to understand how the boundary condition affects the behavior of the solutions when (epsilon) is close to (0). The present paper extends to the planar case the results of [36] dealing with the case of dimension (ngeq 3).
For more information see https://ejde.math.txstate.edu/Volumes/2023/57/abstr.html
{"title":"Asymptotic analysis of perturbed Robin problems in a planar domain","authors":"Paolo Musolino, Martin Dutko, Gennady Mishuris","doi":"10.58997/ejde.2023.57","DOIUrl":"https://doi.org/10.58997/ejde.2023.57","url":null,"abstract":"We consider a perforated domain (Omega(epsilon)) of (mathbb{R}^2) with a small hole of size (epsilon) and we study the behavior of the solution of a mixed Neumann-Robin problem in (Omega(epsilon)) as the size (epsilon) of the small hole tends to (0). In addition to the geometric degeneracy of the problem, the nonlinear (epsilon)-dependent Robin condition may degenerate into a Neumann condition for (epsilon=0) and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as (epsilon) tends to (0) and to understand how the boundary condition affects the behavior of the solutions when (epsilon) is close to (0). The present paper extends to the planar case the results of [36] dealing with the case of dimension (ngeq 3).
 For more information see https://ejde.math.txstate.edu/Volumes/2023/57/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136024315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically.
For mote information see https://ejde.math.txstate.edu/Volumes/2023/58/abstr.html
{"title":"Non-local fractional boundary value problems with applications to predator-prey models","authors":"Michal Feckan, Kateryna Marynets","doi":"10.58997/ejde.2023.58","DOIUrl":"https://doi.org/10.58997/ejde.2023.58","url":null,"abstract":"We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically.
 For mote information see https://ejde.math.txstate.edu/Volumes/2023/58/abstr.html
","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136024786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Sobolev critical Schrodinger-Bopp-Podolsky system $$displaylines{ -Delta u+phi u=lambda u+mu|u|^{p-2}u+|u|^4uquad text{in }mathbb{R}^3,cr -Deltaphi+Delta^2phi=4pi u^2quad text{in } mathbb{R}^3, }$$ under the mass constraint (int_{mathbb{R}^3}u^2,dx=c ) for some prescribed (c>0), where (20) is a parameter, and (lambdainmathbb{R}) is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions. For more inofrmation see https://ejde.math.txstate.edu/Volumes/2023/56/abstr.html
{"title":"Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems","authors":"Yuxin Li, Xiaojun Chang, Zhaosheng Feng","doi":"10.58997/ejde.2023.56","DOIUrl":"https://doi.org/10.58997/ejde.2023.56","url":null,"abstract":"We study the Sobolev critical Schrodinger-Bopp-Podolsky system $$displaylines{ -Delta u+phi u=lambda u+mu|u|^{p-2}u+|u|^4uquad text{in }mathbb{R}^3,cr -Deltaphi+Delta^2phi=4pi u^2quad text{in } mathbb{R}^3, }$$ under the mass constraint (int_{mathbb{R}^3}u^2,dx=c ) for some prescribed (c>0), where (20) is a parameter, and (lambdainmathbb{R}) is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions.\u0000For more inofrmation see https://ejde.math.txstate.edu/Volumes/2023/56/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42598070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By using a two-point boundary-value problem and a Schauder's fixed point theorem, we obtain traveling wave solutions connecting ((0,0,0)) to an unknown positive steady state for speed (cgeq c^{ast}=max{2,2sqrt{d_2r_2},2sqrt{d_3r_3}}). Then we present some asymptotic behaviors of traveling wave solutions. In particular we show that the nonlocal effects have a great influence on the final state of traveling wave solutions at (-infty). For more information see https://ejde.math.txstate.edu/Volumes/2023/55/abstr.html
{"title":"Traveling wave solutions for three-species nonlocal competitive-cooperative systems","authors":"Hong-Jie Wu, Bang-Sheng Han, Shao-yue Mi, Liang-Bin Shen","doi":"10.58997/ejde.2023.55","DOIUrl":"https://doi.org/10.58997/ejde.2023.55","url":null,"abstract":"By using a two-point boundary-value problem and a Schauder's fixed point theorem, we obtain traveling wave solutions connecting ((0,0,0)) to an unknown positive steady state for speed (cgeq c^{ast}=max{2,2sqrt{d_2r_2},2sqrt{d_3r_3}}). Then we present some asymptotic behaviors of traveling wave solutions. In particular we show that the nonlocal effects have a great influence on the final state of traveling wave solutions at (-infty). \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/55/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45357779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we consider a singular elliptic problem with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent. By using variational methods and Palais-Smale condition, we show the existence of at least two nontrivial solutions. The result depends crucially on the parameters (a,b,N,beta,gamma,lambda,mu). For more information see https://ejde.math.txstate.edu/Volumes/2023/54/abstr.html
{"title":"Existence of solutions for singular elliptic problems with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent","authors":"M. E. O. E. El Mokhtar","doi":"10.58997/ejde.2023.54","DOIUrl":"https://doi.org/10.58997/ejde.2023.54","url":null,"abstract":"In this article, we consider a singular elliptic problem with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent. By using variational methods and Palais-Smale condition, we show the existence of at least two nontrivial solutions. The result depends crucially on the parameters (a,b,N,beta,gamma,lambda,mu).\u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/54/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44301555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we consider the viscoelastic wave equation $$ u_{tt}-Delta u+int_0^{t}g(t-s)Delta u(s)ds+a| u_t| ^{m(cdot )-2}u_t=0 $$ with a nonlinear feedback having a variable exponent (m(x)). We investigate the interaction between the two types of damping and establish an optimal decay result under very general assumptions on the relaxation function (g). We construct explicit formulae which provide faster energy decay rates than the ones already existing in the literature. For more information see https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html
{"title":"Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent","authors":"M. I. Mustafa","doi":"10.58997/ejde.2023.53","DOIUrl":"https://doi.org/10.58997/ejde.2023.53","url":null,"abstract":"In this article, we consider the viscoelastic wave equation $$ u_{tt}-Delta u+int_0^{t}g(t-s)Delta u(s)ds+a| u_t| ^{m(cdot )-2}u_t=0 $$ with a nonlinear feedback having a variable exponent (m(x)). We investigate the interaction between the two types of damping and establish an optimal decay result under very general assumptions on the relaxation function (g). We construct explicit formulae which provide faster energy decay rates than the ones already existing in the literature. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45970323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article studies a fourth-order elliptic problem with and without an eigenvalue parameter. New criteria for the existence and nonexistence of positive solution are established under some sublinear conditions which involve the principal eigenvalues of the corresponding linear problems. The interesting point is that the nonlinear term (f) is involved in the second-order derivative explicitly. For more information see https://ejde.math.txstate.edu/Volumes/2023/52/abstr.html
{"title":"Existence and nonexistence of positive solutions for fourth-order elliptic problems","authors":"Meiqiang Feng, Haiping Chen","doi":"10.58997/ejde.2023.52","DOIUrl":"https://doi.org/10.58997/ejde.2023.52","url":null,"abstract":"This article studies a fourth-order elliptic problem with and without an eigenvalue parameter. New criteria for the existence and nonexistence of positive solution are established under some sublinear conditions which involve the principal eigenvalues of the corresponding linear problems. The interesting point is that the nonlinear term (f) is involved in the second-order derivative explicitly. For more information see https://ejde.math.txstate.edu/Volumes/2023/52/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136043996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we establish the existence of solutions for a fourth-order four-point non-linear boundary value problem (BVP) which arises in bridge design, $$displaylines{ - y^{(4)}( s)-lambda y''( s)=mathcal{F}( s, y( s)), quad sin(0,1),cry(0)=0,quad y(1)= delta_1 y(eta_1)+delta_2 y(eta_2),cr y''(0)=0,quad y''(1)= delta_1 y''(eta_1)+delta_2 y''(eta_2), }$$ where (mathcal{F} in C([0,1]times mathbb{R},mathbb{R})), (delta_1, delta_2>0), (0
{"title":"Existence and uniqueness results for fourth-order four-point BVP arising in bridge design in the presence of reverse ordered upper and lower solutions","authors":"Nazia Urus, Amit Verma","doi":"10.58997/ejde.2023.51","DOIUrl":"https://doi.org/10.58997/ejde.2023.51","url":null,"abstract":"In this article, we establish the existence of solutions for a fourth-order four-point non-linear boundary value problem (BVP) which arises in bridge design, $$displaylines{ - y^{(4)}( s)-lambda y''( s)=mathcal{F}( s, y( s)), quad sin(0,1),cry(0)=0,quad y(1)= delta_1 y(eta_1)+delta_2 y(eta_2),cr y''(0)=0,quad y''(1)= delta_1 y''(eta_1)+delta_2 y''(eta_2), }$$ where (mathcal{F} in C([0,1]times mathbb{R},mathbb{R})), (delta_1, delta_2>0), (0<eta_1le eta_2 <1), (lambda=zeta_1+zeta_2 ), where (zeta_1) and (zeta_2) are the real constants. We have explored all gathered (0<zeta_1<zeta_2), (zeta_1<0<zeta_2), and ( zeta_1<zeta_2<0 ). We extend the monotone iterative technique and establish the existence results with reverse ordered upper and lower solutions to fourth-orderfour-point non-linear BVPs. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/51/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46165150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We extend the results in Kloeden-Simsen [CPAA 2014] to (p(x,t))-Laplacian problems on time-dependent Lebesgue spaces withvariable exponents. We study the equation $$displaylines{ frac{partial u_lambda}{partial t}(t)-operatorname{div}big(D_lambda(t,x)|nabla u_lambda(t)|^{p(x,t)-2}nabla _lambda(t)big)+|u_lambda(t)|^{p(x,t)-2}u_lambda(t) =B(t,u_lambda(t)) }$$on a bounded smooth domain (Omega) in (mathbb{R}^n),(ngeq 1), with a homogeneous Neumann boundary condition, where the exponent (p(cdot)in C(bar{Omega}times [tau,T],mathbb{R}^+)) satisfies (min p(x,t)>2), and (lambdain [0,infty)) is a parameter. For more information see https://ejde.math.txstate.edu/Volumes/2023/50/abstr.html
{"title":"Evolution equations on time-dependent Lebesgue spaces with variable exponents","authors":"J. Simsen","doi":"10.58997/ejde.2023.50","DOIUrl":"https://doi.org/10.58997/ejde.2023.50","url":null,"abstract":"We extend the results in Kloeden-Simsen [CPAA 2014] to (p(x,t))-Laplacian problems on time-dependent Lebesgue spaces withvariable exponents. We study the equation $$displaylines{ frac{partial u_lambda}{partial t}(t)-operatorname{div}big(D_lambda(t,x)|nabla u_lambda(t)|^{p(x,t)-2}nabla _lambda(t)big)+|u_lambda(t)|^{p(x,t)-2}u_lambda(t) =B(t,u_lambda(t)) }$$on a bounded smooth domain (Omega) in (mathbb{R}^n),(ngeq 1), with a homogeneous Neumann boundary condition, where the exponent (p(cdot)in C(bar{Omega}times [tau,T],mathbb{R}^+)) satisfies (min p(x,t)>2), and (lambdain [0,infty)) is a parameter.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/50/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42410358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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