MULTIPLE SOLUTIONS FOR A CLASS OF NONLINEAR NEUMANN EIGENVALUE PROBLEMS

作者：Gasinski Leszek^*; Papageorgiou Nikolaos S

来源：Communications on Pure and Applied Analysis, 2014, 13(4): 1491-1512.

DOI：10.3934/cpaa.2014.13.1491

• Smooth solutions of constant sign
• nodal solutions
• first nonzero eigenvalue
• mountain pass theorem
• critical groups
• negative gradient flow
• flow invariance

We consider a parametric nonlinear equation driven by the Neumann p-Laplacian. Using variational methods we show that when the parameter lambda > (lambda) over cap (1) (where (lambda) over cap (1) is the first nonzero eigenvalue of the negative Neumann p-Laplacian), then the problem has at least three nontrivial smooth solutions, two of constant sign (one positive and one negative) and the third nodal. In the semilinear case (i.e., p = 2), using Morse theory and flow invariance argument, we show that the problem has three nodal solutions.

• 出版日期2014-7