一类超线性(p,2)-拉普拉斯Dirichlet问题的非平凡解

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (1): 92-101.

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Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems

Pei Ruichang¹, Zhang Jihui², Ma Caochuan¹

1. School of Mathematics and Statistics, Tianshui Normal University, Gansu Tianshui 741001;
2. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097

Received:2016-03-09 Revised:2016-10-27 Online:2017-02-26 Published:2017-02-26
Supported by:
Supported by the NSFC (11661070, 11571176), the Natural Science Foundation of Gansu Province (1506RJZE114, 1606RJYE237) and the Scientific Research Foundation of the Higher Education Institutions of Gansu Province (2015A-129, 2015A-131)

Abstract

Abstract:

In this paper, we consider a class of particular (p,2)-Laplacian Dirichlet problem with nonlinearity which is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition at infinity. Some existence results for nontrivial solution are established by Morse theory in the general case 2 < p < N and similar results are also established by combining Morse theory with Moser-Trudinger inequality when p=N.

Key words: (p,2)-Laplacian Dirichlet problem, Morse theory, Subcritical exponential growth, Improved subcritical polynomial growth

CLC Number:

O175.23

Pei Ruichang, Zhang Jihui, Ma Caochuan. Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems[J].Acta mathematica scientia,Series A, 2017, 37(1): 92-101.

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Nontrivial Solutions for a Class of Superlinear (p, 2)-Laplacian Dirichlet Problems

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