Infinitely many solutions for a class of fourth-order partially sublinear 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

Infinitely Many Solutions for a Class of Sublinear Schrödinger Equations

where V : R → R and f : R × R → R. In the past several decades, the existence and multiplicity of nontrivial solutions for problem (1.1) have been extensively investigated in the literature with the aid of critical point theory and variational methods. Many papers deal with the autonomous case where the potential V and the nonlinearity f are independent of x, or with the radially symmetric case...

Existence results of infinitely many solutions for a class of p(x)-biharmonic problems

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.

Infinitely many solutions for a class of $p$-biharmonic‎ ‎equation in $mathbb{R}^N$

‎Using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{R}^N$‎. ‎The existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $V(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.