Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Advances in Nonlinear Analysis - Tập 5 Số 1 - Trang 27-55 - 2016
Patrizia Pucci1, Mingqi Xiang2, Binlin Zhang3
1Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy
2College of Science, Civil Aviation University of China, Tianjin, 300300, P.R. China
3Department of Mathematics , Heilongjiang Institute of Technology , Harbin , 150050 , P. R. China

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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.

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Advances in Nonlinear Analysis

Tập 5 Số 1

27-55

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