MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN RN

doi:10.1016/S0252-9602(18)30756-2

Abstract

Abstract:

In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type
-ε^pM(ε^p-N ∫_R^N|▽u|^p)△_pu + V (x)|u|^p-2u=f(u)
in R^N, where △_p is the p-Laplacian operator, 1< p < N, M:R⁺→ R⁺ and V:R^N → R⁺ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.

Key words: Schrödinger-Kirchhoff type equation, variational methods, multiple positive solutions, concentrating solution, penalization method

Huifang JIA, Gongbao LI. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J].Acta mathematica scientia,Series B, 2018, 38(2): 391-418.

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MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N

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