Maximum principle and existence of solutions for non necessarily cooperative systems involving Schrödinger operators

Abstract

ABSTRACT. In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (φ q -positivity) for non cooperative systems.

Optimality of Distributed Control for <i>n × n</i> Hyperbolic Systems with an Infinite Number of Variables

“…given by the follo (22) Theorem 4: The necessary and sufficient conditions for optimality of the control problem (20), (21) and (22) Thus there are no constraints on then the inequality (26) is equivalent to  the type of system (non-cooperative, cooperative), tion, many of variations on the above ssible to study with the help of Lions 008, pp. 37-48.…”

“…Some applications of optimal control problem for systems involving Schrodinger operators are introduced for example in [17][18][19][20][21].…”