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 ℝN. 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.
Funding source: MIUR
Award Identifier / Grant number: Aspetti variazionali e perturbativi nei problemi differenziali nonlineari
Funding source: INDAM-GNAMPA
Award Identifier / Grant number: Prot_2015_000368
Funding source: Fundamental Research Funds for the Central Universities
Award Identifier / Grant number: 3122015L014
Funding source: Natural Science Foundation of Heilongjiang Province of China
Award Identifier / Grant number: A201306
Funding source: Research Foundation of Heilongjiang Educational Committee
Award Identifier / Grant number: 12541667
Funding source: Doctoral Research Foundation of Heilongjiang Institute of Technology
Award Identifier / Grant number: 2013BJ15
© 2016 by De Gruyter
