scholarly journals Infinitely Many Solutions for a Robin Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-9
Author(s):  
Aixia Qian ◽  
Chong Li
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Boundary Value ◽  
Elliptic Problems ◽  
Infinitely Many Solutions ◽  
Weaker Conditions ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

By combining the embedding arguments and the variational methods, we obtain infinitely many solutions for a class of superlinear elliptic problems with the Robin boundary value under weaker conditions.

scholarly journals Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

2017 ◽  
Vol 15 (1) ◽  
pp. 1549-1557 ◽  
Author(s):  
Yuhua Long ◽  
Baoling Zeng
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Parameter Dependence ◽  
Invariant Sets ◽  
Sign Changing Solutions ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

Abstract In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

scholarly journals Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
I. Ibrango ◽  
S. Ouaro
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Boundary Value ◽  
Monotone Operators ◽  
Robin Boundary Conditions ◽  
Anisotropic Problems ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak solutions converges to a measurable function which is the entropy solution of the anisotropic Robin boundary value problem.

scholarly journals A Variational Approach to Perturbed Discrete Anisotropic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Amjad Salari ◽  
Giuseppe Caristi ◽  
David Barilla ◽  
Alfio Puglisi
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Results ◽  
Anisotropic Equation

We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

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