Existence and multiplicity of entire solutions for fractional <i>p</i> -Kirchhoff equations 论文

详细信息

发表期刊/会议

Advances in Nonlinear Analysis

发表日期

2015-09-16

发表年份

2015

摘要

Abstract The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p -Laplacian operator in ℝ N . By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers of the weights. Finally, existence of infinitely many pair of entire solutions is obtained by genus theory. Last but not least, the paper covers a main feature of Kirchhoff problems which is the fact that the Kirchhoff function M can be zero at zero. The results of this paper are new even for the standard stationary Kirchhoff equation involving the Laplace operator.