Abstract
Existence of weak solutions for a class of nonlinear elliptic systems is obtained under the certain Landesman-Lazer-type conditions by variational method.
Highlights
Introduction and main resultsIn this paper, we consider the existence of weak solutions for the following gradient elliptic systems: ⎧ ⎪⎪⎨– pu = λ a(x)|u|p– u + λ b(x) β + |u|α |v|β v
Existence of weak solutions for a class of nonlinear elliptic systems is obtained under the certain Landesman-Lazer-type conditions by variational method
1 Introduction and main results In this paper, we consider the existence of weak solutions for the following gradient elliptic systems:
Summary
Abstract Existence of weak solutions for a class of nonlinear elliptic systems is obtained under the certain Landesman-Lazer-type conditions by variational method. The coefficient functions a, b, c ∈ C( ) ∩ L∞( ) satisfy one of the following conditions: (A ) a+ = , where a+(x) := max{a(x), }; (A ) c+ = ; (A ) a = c = and b+ = . The Landesman-Lazer-type conditions were introduced by Landesman and Lazer in [ ], where they considered the existence of weak solutions for the resonant elliptic problems, and were widely used and extended (see [ – ] and their references).
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