A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue Problems

作者：Kyritsi Sophia Th^*; Papageorgiou Nikolaos S

来源：Funkcialaj Ekvacioj-Serio Internacia, 2012, 55(1): 1-15.

• p-Laplacian
• Nonlinear maximum principle
• Local minimizers
• Nonlinear regularity
• Bifurcation-type theorem
• Positive solution

We consider a nonlinear Neumann eigenvalue problem driven by the p-Laplacian and with a (p - 1)-sublinear reaction. Using variational methods together with suitable truncation techniques, we prove a bifurcation-type theorem for the eigenvalue problem. Namely, we show that there is a critical parameter value lambda(*) %26gt; 0 such that for all lambda %26gt; lambda(*) the problem has at least two positive solutions, for lambda = lambda(*) there is at least one positive solution and for A lambda is an element of (0, lambda(*)) no positive solutions exist.

• 出版日期2012-4
• 单位中国人民解放军海军大连舰艇学院