Georgian Mathematical Journal 13 (2006), No. 3, 433--445
Copyright Heldermann Verlag 2006
Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
Teodora-Liliana Dinu
Dept. of Mathematics, Fratii Buzesti College, Bd. Stirbei-Voda 5, 200352 Craiova, Romania
tldinu@gmail.com
We establish the existence of an entire solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof is based on the critical point theory in the sense of Clarke and we apply the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of P. H. Rabinowitz [Z. Angew. Math. Phys. 43 (1992) 270--291] on the existence of entire solutions of the nonlinear Schrödinger equation.
Keywords: Nonlinear elliptic system, entire solution, Lipschitz functional, Clarke generalized gradient.
MSC: 35J50, 49J52, 58E05
[ Fulltext-pdf (232 KB)] for subscribers only.