p(x)-LAPLACIAN EQUATIONS WITH SUBCRITICAL GROWTH WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION

被引：0

作者：

Xia, Qi ^{[1
]}

Feng, Xinlong ^{[1
]}

He, Yinnian ^{[1
,2
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年

关键词：

p(x)-Laplacian equation; subcritical growth; the Mountain-Pass Theorem; without the (AR) condition; SUPERLINEAR PROBLEMS; R-N; EXISTENCE; THEOREMS; LAPLACIAN;

D O I：

10.3934/dcdss.2024146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to deal with the superlinear elliptic problem, which does not satisfy the Ambrosetti-Rabinowitz condition near infinity. With the Hahn-Banach Theorem, we overcome the difficulty that the Palais-Smale sequences of the functional are bounded. Some existence and multiplicity results for nontrivial solutions are obtained by using the Mountain-Pass Theorem and the Fountain Theorem. Our work is to promote and innovate on the basis of a recent result of [32].

引用

页码：1805 / 1819

页数：15

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