Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

2021 ◽  
Vol 110 (1-2) ◽  
pp. 226-241
Author(s):  
V. N. Pavlenko ◽  
D. K. Potapov
Keyword(s):  
Elliptic Systems ◽  
Discontinuous Nonlinearities

Variational method for elliptic systems with discontinuous nonlinearities

2021 ◽  
Vol 212 (5) ◽  
Author(s):  
Vyacheslav Nikolaevich Pavlenko ◽  
Dmitriy Konstantinovich Potapov
Keyword(s):  
Variational Method ◽  
Elliptic Systems ◽  
Discontinuous Nonlinearities

Sublinear elliptic systems with discontinuous nonlinearities

1992 ◽  
Vol 44 (1-2) ◽  
pp. 37-50
Author(s):  
F.J.S.A. Correa ◽  
J.V.A. Gonçalves
Keyword(s):  
Elliptic Systems ◽  
Discontinuous Nonlinearities

scholarly journals ENTIRE SOLUTIONS OF SCHRÖDINGER ELLIPTIC SYSTEMS WITH DISCONTINUOUS NONLINEARITY AND SIGN‐CHANGING POTENTIAL

2006 ◽  
Vol 11 (3) ◽  
pp. 229-242 ◽  
Author(s):  
T. L. Dinu
Keyword(s):  
Blow Up ◽  
Elliptic Systems ◽  
Point Theory ◽  
Entire Solution ◽  
Mountain Pass Lemma ◽  
Discontinuous Nonlinearity ◽  
Entire Solutions ◽  
Discontinuous Nonlinearities ◽  
Locally Lipschitz ◽  
Schrödinger Systems

We establish the existence of an entire solution for a class of stationary Schrodinger 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 the result of Rabinowitz [16] on the existence of entire solutions of the nonlinear Schrodinger equation.

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