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

作者：Saeedi, Ghulamullah^*; Waseel, Farhad; Jalal, Hadia

来源：Communications on Pure and Applied Analysis, 2022, 21(9): 3193-3211.

DOI：10.3934/cpaa.2022096

• Quasilinear elliptic equations
• Mountain-Pass lemma
• critical points
• nontrivial solutions
• nonexistence of nontrivial solution

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.