( p ,2)-equations asymmetric at both zero and infinity

Advances in Nonlinear Analysis

article

Nikolaos S. Papageorgiou¹  Vicenţiu D. Rădulescu²  Dušan D. Repovš⁴ 

[1] Department of Mathematics, National Technical University, Zografou Campus;Institute of Mathematics “Simion Stoilow” of the Romanian Academy;Department of Mathematics, University of Craiova;Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana

关键词: asymmetric reaction;    resonance;    Fučik spectrum;    constant sign solutions;    nodal solution;    critical groups;    Morse relation;   

DOI  :  10.1515/anona-2017-0195

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider a (p,2){(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p -Laplacian and a Laplacian with p>2{p>2}. The reaction term is (p-1){(p-1)}-linear, but exhibits asymmetric behavior at ±∞{\pm\infty} and at 0±{0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).

【 授权许可】

CC BY