Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations

Abstract

The paper deals with existence, multiplicity and asymptotic behavior of entire solutions for a series of stationary Kirchhoff fractional p-Laplacian equations. The existence presents several difficulties due to the intrinsic lack of compactness arising from different reasons, and the suitable strategies adopted to overcome the technical hurdles depend on the specific problem under consideration. The results of the paper extend in several directions recent theorems. Furthermore, the main assumptions required in the paper weaken the hypotheses used in the recent literature on stationary Kirchhoff fractional problems. Some equations treated in the paper cover the so-called degenerate case that is the case in which the Kirchhoff function M is zero at zero. In other words, from a physical point of view, when the base tension of the string modeled by the equation is zero, it is a very realistic case. Last but not least no monotonicity assumption is required on M, and also this aspect makes the models more believable in several physical applications.