Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

作者：Papageorgiou Nikolaos S; Radulescu Vicentiu D^*; Repovs Dusan D

来源：Journal of Optimization Theory and Applications, 2017, 175(2): 293-323.

DOI：10.1007/s10957-017-1173-5

• Locally Lipschitz function
• Clarke subdifferential
• Resonance
• Extremal constant sign solutions
• Nodal solutions
• Nonlinear nonhomogeneous differential operator

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).

• 出版日期2017-11