Existence of solutions for Dirichlet elliptic problems with discontinuous nonlinearity

2020 ◽  
Vol 197 ◽  
pp. 111848
Author(s):  
Ziqing Yuan ◽  
Jianshe Yu
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Discontinuous Nonlinearity

scholarly journals Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities

2019 ◽  
Vol 21 (1) ◽  
pp. 77-93
Author(s):  
Yansheng Shen
Keyword(s):  
Variational Methods ◽  
Minimization Problem ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Type Equation ◽  
Nontrivial Solutions ◽  
Critical Nonlinearities

Abstract In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝ N {\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential. Using variational methods, we investigate the attainability of the corresponding minimization problem, and then obtain the existence of solutions. We also consider another Choquard type equation involving the p-Laplacian and critical nonlinearities in ℝ N {\mathbb{R}^{N}} .

scholarly journals Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

2019 ◽  
Vol 38 (4) ◽  
pp. 31-50
Author(s):  
M. Bagheri ◽  
Ghasem A. Afrouzi
Keyword(s):  
Local Minimum ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Hardy Potential ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Minimum Theorem

In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

Existence of solutions for some nonlinear elliptic problems involving Minty’s lemma

2018 ◽  
Vol 68 (2) ◽  
pp. 513-534
Author(s):  
Mohammed Al-Hawmi ◽  
Abdelmoujib Benkirane ◽  
Hassane Hjiaj ◽  
Abdelfattah Touzani
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Minty’S Lemma

scholarly journals A class of nonlinear elliptic problems with nonconvex constraints and applications

1998 ◽  
Vol 41 (2) ◽  
pp. 333-357
Author(s):  
N. Chemetov ◽  
J. F. Rodrigues
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Monotone Operators ◽  
Global Constraints ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Biological Population ◽  
Unilateral Problems ◽  
Nonlocal Terms ◽  
Nonconvex Constraints

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.

scholarly journals Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$

2013 ◽  
Vol 112 (1) ◽  
pp. 129 ◽  
Author(s):  
Claudianor O. Alves ◽  
Rúbia G. Nascimento
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Discontinuous Nonlinearity ◽  
Concentration Of Solutions

Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.

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