EXISTENCE OF SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH A PARAMETER

摘要

This paper is concerned with the existence of nontrivial solutions for the quasilinear elliptic equation @@@ [GRAPHICS] @@@ where 3/4 <= alpha <= 1 and V (x) is a positive continuous function. Using Mountain-Pass lemma we establish the existence of nontrivial solutions. When q >= 2 alpha 2*, by using a Pohozaev type variational identity we prove that the equation has no nontrivial solutions.

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