没有Landesman-Lazer 型条件的拟线性强振动方程之无穷多解

Abstract

Abstract:

The famous Landesman-Lazer conditions is used to be applied in solving the existent solution for elliptic resonant equations. In this paper, the author is by using the property of the space of the first eigenfunctions and the technique of genus to give an existence theorem for infinitely many solutions of the strong resonant equation -Δ_pu=λ₁|u|^p-2u+g(x, u) without any Landesman-Lazer conditions, which extends some recent results from single or several solutions to infinitely many solutions.

Key words: p-Laplacian operator, Deformation Lemma, Palais-Smale condition

CLC Number:

35J65

RAO Ruo-Feng, WANG Xiong-Rui. Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions[J].Acta mathematica scientia,Series A, 2012, 32(4): 744-752.

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Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions

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