Nonlinear Elliptic Eigenvalue Problems with Discontinuities
In this paper we study the existence of solution for two different eigenvalue problems. The first is nonlinear and the second is semilinear. Our approach is based on results from the nonsmooth critical point theory. In the first theorem we prove the existence of at least two nontrivial solutions when λ is in a half-axis. In the second theorem (based on a nonsmooth variant of the generalized mountain pass theorem), we prove the existence of at least one nontrivial solution for every λ∈R. © 1999 Academic Press.
Compact embedding, Critical point, Locally Lipschitz functions, Maximal monotone operators, Mountain Pass Theorem, Nonsmooth Palais-Smale condition, Rayleigh quotient, Subdifferential
Hu, Shouchuan, Nikolaos C. Kourogenis, and Nikolaos S. Papageorgiou. "Nonlinear elliptic eigenvalue problems with discontinuities." Journal of mathematical analysis and applications 233, no. 1 (1999): 406-424.
Journal of Mathematical Analysis and Applications