Infinitely Many Solutions For A Fourth-order Kirchhoff Type Elliptic Problem

Abstract

This paper studies the existence of infinitely many solutions for a fourth-order Kirchhoff type elliptic problem () ∫ Our technical approach is based on Ricceri's principle variational.

Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator

“…When p(x) = p in problem (1), the corresponding conclusions were given in [4]. The study of a nonlocal type problem involving p-biharmonic operator has been extended to the p(x)-biharmonic operator and reached more general conclusions.…”

“…In [3], when the nonlinear term f (x, u) satisfying the (AR) condition, using the mountain pass theorem and local minimum theorem, two non-trivial solutions of the p-biharmonic system have been obtained. The authors in [4] researched the same problem in [3] and obtained multiple solutions according to Ricceri's variational Principle. The p(x)-biharmonic problem is the general form of the p-biharmonic problem. The operator is no longer a satisfied homogeneous and pointwise identity.…”

One solution for nonlocal fourth order equations

“…The function f represents the force that the foundation exerts on the beam and M Ω ∇u p dx models the effects of the small changes in the length of the beam. Recently, many researchers have paid their attention to fourth-order Kirchhoff-type problems, we refer the reader to [16,34,42,43] and the references therein. In [42], using the mountain pass theorem, Wang and An established the existence and multiplicity of solutions for the following fourth-order nonlocal elliptic problem…”

On the existence of solutions for a class of fourth order elliptic equations of Kirchhoff type with variable exponent

“…We point out that if p(.) is a constant then problem (1) has been studied by many authors in recent years, we refer to some interesting papers [3,8,15,19,23,27,28,29]. In [29], Wang and An considered the following fourth-order elliptic equation…”

“…Some extensions regarding these results can be found in [3,8,15,27] in which the authors considered problem (2) in R N or the nonlinearities involved critical exponents. In [19,23], problem (1) has been studied in the general case when p(.) = p ∈ (1, +∞) is a constant.…”