Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419481 | Journal of Mathematical Analysis and Applications | 2011 | 14 Pages |
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 inclusionâÎpuââF(x,u)â|u|pâ2uin Ω with the boundary condition|âu|pâ2âuâνâa(u+)pâ1âb(uâ)pâ1+âG(x,u)on âΩ. 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 C1(Ω¯)-minimizers and local W1,p(Ω)-minimizers of nonsmooth functionals.