Abstract
The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.
Highlights
The aim of this paper is to establish the existence of infinitely many weak solutions for the following mixed boundary value system with (p1, . . . , pm)-Laplacian
Among the papers which have dealt with the nonlinear mixed boundary value problems we cite [1, 3, 10, 13]
We investigate the existence of infinitely many weak solutions for system (1.1) by using
Summary
The aim of this paper is to establish the existence of infinitely many weak solutions for the following mixed boundary value system with (p1, . . . , pm)-Laplacian. The aim of this paper is to establish the existence of infinitely many weak solutions for the following mixed boundary value system with We investigate the existence of infinitely many weak solutions for system (1.1) by using. 1 γ [, the following alternatives hold: either (b1) Φ − λΨ possesses a global minimum, or (b2) there is a sequence {un} of critical points (local minima) of Φ − λΨ such that limn→+∞ Φ(un) = +∞. Many authors proved the existence of infinitely many solutions by using the theorem above for different problems see for example [2, 4–9, 11]. At first we prove the existence of an unbounded sequence of weak solutions of system (1.1) under some hypotheses on the behaviour of potential F at infinity (see Theorem 3.1). We obtain the existence of infinitely many weak solutions for autonomous case (see Corollary 3.4)
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