Existence and multiplicity results for critical growth polyharmonic elliptic systems

Abstract

In the present paper, we deal with the existence and multiplicity of nontrivial solutions for a class of polyharmonic elliptic systems with Sobolev critical exponent in a bounded domain. Some new existence and multiplicity results are obtained. Our proofs are based on the Nehari manifold and Ljusternik–Schnirelmann theory. Copyright © 2013 John Wiley & Sons, Ltd.

Infinitely many solutions for polyharmonic equations of p(x)‐Laplace type

“…11 The authors were concerned with fourth-order differential equations that arise from the study of beam deflection problems on nonlinear elastic foundation. The p(x)-polyharmonic operator that takes into account higher order Kirchhoff equations involving the variable exponent related to modeling of so-called electrorheological fluids was investigated in Colasuonno and Pucci 1 ; see also Autuori et al 12 Colasuonno and Pucci 1 establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p(x)-polyharmonic Kirchhoff equations, including the new delicate degenerate case via the symmetric mountain pass theorem (see, e.g., previous studies [13][14][15][16][17][18][19] ).…”