Infinitely Many Solutions for a Fourth–order Nonlinear Elliptic System
نویسندگان
چکیده
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 results by Y. Ye and C. Tang (J. Math. Anal. Appl. 394, 841-854, 2012) to fourth-order nonlinear elliptic system. Mathematics subject classification (2010): 26D15, 26A51, 32F99, 41A17.
منابع مشابه
Existence of Infinitely Many Solutions for Perturbed Kirchhoff Type Elliptic Problems with Hardy Potential
In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.
متن کاملExistence of Infinitely Many Solutions for Fourth-order Equations Depending on Two Parameters
By using variational methods and critical point theory, we establish the existence of infinitely many classical solutions for a fourth-order differential equation. This equation has nonlinear boundary conditions and depends on two real parameters.
متن کاملExistence of Infinitely Many Large Solutions for a Class of Fourth - Order Elliptic Equations In
متن کامل
Existence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کاملExistence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کامل