Multiplicity of Solutions for Fourth-Order Elliptic Equations with p-Laplacian and Mixed Nonlinearity

2020 ◽  
Vol 17 (2) ◽  
Author(s):  
A. H. Benhanna ◽  
A. Choutri
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Multiplicity Of Solutions ◽  
Mixed Nonlinearity ◽  
Fourth Order Elliptic Equations

scholarly journals A class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$

2021 ◽  
pp. 1-16
Author(s):  
Zijian Wu ◽  
Haibo Chen
Keyword(s):  
Variational Principle ◽  
Fourth Order ◽  
Ground State ◽  
Elliptic Equations ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
Ekeland Variational Principle ◽  
Multiplicity Of Solutions ◽  
Concave And Convex Nonlinearities ◽  
Fourth Order Elliptic Equations

In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under the appropriate assumption, we prove that there are at least two solutions for the equation by Nehari manifold and Ekeland variational principle, one of which is the ground state solution.

Sign in / Sign up

Export Citation Format

Share Document