Multiple Solutions for Nonlinear Periodic Problems

Canadian mathematical bulletin

Nikolaos S. Papageorgiou¹  Sophia Th. Kyritsi² 

[1] National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece;Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece

关键词: $C$-condition;    mountain pass theorem;    critical groups;    strong deformation retract;    contractible space;    homotopy invariance;   

DOI  :  10.4153/CMB-2011-154-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We consider a nonlinear periodic problem driven by anonlinear nonhomogeneous differential operator and aCarathéodory reaction term $f(t,x)$ that exhibits a$(p-1)$-superlinear growth in $x in mathbb{R}$ near $pminfty$ and near zero.A special case of the differential operator is the scalar$p$-Laplacian. Using a combination of variational methods based onthe critical point theory with Morse theory (critical groups), weshow that the problem has three nontrivial solutions, two of whichhave constant sign (one positive, the other negative).

【 授权许可】

Unknown