Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:377

Article

Winkert, Patrick

关键词: Clarke's generalized gradient;    Mountain-Pass Theorem;    Multiple solutions;    Sub-supersolution method;    p-Laplacian;   

DOI  :  10.1016/j.jmaa.2010.10.029

来源: Elsevier

【 摘 要 】

The main goal of this paper is to present multiple solution results for elliptic inclusions of Clarke's gradient type under nonlinear Neumann boundary conditions involving the p-Laplacian and set-valued nonlinearities. To be more precise, we study the inclusion -Delta(p)u is an element of partial derivative F(x, u) - vertical bar u vertical bar(p-2)u in Omega with the boundary condition vertical bar del u vertical bar(p-2)partial derivative u/partial derivative v is an element of a(u(+))(p-1) - b(u(-))(p-1) + partial derivative G(x, u) on partial derivative Omega. We prove the existence of two constant-sign solutions and one sign-changing solution depending on the parameters a and b. Our approach is based on truncation techniques and comparison principles for elliptic inclusions along with variational tools like the nonsmooth Mountain-Pass Theorem, the Second Deformation Lemma for locally Lipschitz functionals as well as comparison results of local C-1 ((Omega) over bar)-minimizers and local W-1.p(Omega)-minimizers of nonsmooth functionals. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free