NONLINEAR DIRICHLET PROBLEMS WITH DOUBLE RESONANCE

被引：0

作者：

Aizicovici, Sergiu ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

Staicu, Vasile ^{[3
,4
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

[2] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

[3] Univ Aveiro, CIDMA, P-3810193 Aveiro, Portugal

[4] Univ Aveiro, Dept Math, P-3810193 Aveiro, Portugal

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2017年 / 16卷 / 04期

关键词：

p-Laplacian; double resonance; nonlinear regularity; critical groups; constant sign and nodal solutions; EQUATIONS;

D O I：

10.3934/cpaa.2017056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a nonlinear Dirichlet problem driven by the sum of a p-Laplacian (p > 2) and a Laplacian and which at +/-infinity is resonant with respect to the spectrum of ( -Delta(p),W-0(1,P)(Omega)) and at zero is resonant with respect to the spectrum of (-Delta,H-0(1) (Omega)) (double resonance). We prove two multiplicity theorems providing three and four nontrivial solutions respectivelly, all with sign information. Our approach uses critical point theory together with truncation and comparison techniques and Morse theory.

引用

页码：1147 / 1168

页数：22

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