Infinitely many solutions for a fourth order singular elliptic problem

Infinitely Many Solutions for a Fourth–order Nonlinear Elliptic System

In this paper we study the existence of solutions for the nonlinear elliptic system ⎪⎪⎨ ⎪⎪⎩ Δu−Δu+V1(x)u = fu(x,u,v), Δv−Δv+V2(x)v = fv(x,u,v), u,v ∈ H(R) x ∈ R , where V1(x) and V2(x) are positive continue functions. Under some assumptions on fu(x,u,v) and fv(x,u,v) , we prove the existence of many nontrivial high and small energy solutions by variant Fountain theorems. This generalizes the re...

Existence of Infinitely Many Large Solutions for a Class of Fourth - Order Elliptic Equations In

Two weak solutions for some singular fourth order elliptic problems

In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-biharmonic operator, subject to Navier boundary conditions in a smooth bounded domain in RN . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct nontrivial weak solutions.

Multiple solutions for a fourth-order nonlinear elliptic problem

The existence of multiple solutions for a class of fourth-order elliptic equation with respect to the generalized asymptotically linear conditions is established by using the minimax method and Morse theory.

Infinitely Many Solutions for a Steklov Problem Involving the p(x)-Laplacian Operator

By using variational methods and critical point theory for smooth functionals defined on a reflexive Banach space, we establish the existence of infinitely many weak solutions for a Steklov problem involving the p(x)-Laplacian depending on two parameters. We also give some corollaries and applicable examples to illustrate the obtained result../files/site1/files/42/4Abstract.pdf