Infinitely many solutions for a fourth-order nonlinear elliptic system

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 Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

and Applied Analysis 3 where a ∈ [0, π), b ∈ C([0, 1], [0, +∞)) and c, γ > 0. It is easy to verify that all conditions ofTheorem 4 are satisfied. So, BVP (1)with the nonlinear term (10) has at least two solutions, one positive and the other negative. Reference [7, Theorem 3.3] can only guarantee a nonzero solution for this example. Theorem 7. Assume that (H1)–(H5) hold. Then, BVP (1) has at lea...

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 of Superlinear Elliptic Equation

and Applied Analysis 3 Lemma 6 (see [17]). Assume that |Ω| < ∞, 1 ≤ p, r ≤ ∞, f ∈ C(Ω×R), and |f(x, u)| ≤ c(1+|u|). Then for every