Existence Solutions for a Weighted Biharmonic Equation with Critical Exponential Growth

被引：6

作者：

Dridi, Brahim ^{[1
]}

Jaidane, Rached ^{[2
]}

机构：

[1] Umm Al Qura Univ, Fac Appl Sci, Dept Math, POB 14035, Holly Makkah 21955, Saudi Arabia

[2] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis, Tunisia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 02期

关键词：

Adams' inequality; Moser-Trudinger's inequality; nonlinearity of exponential growth; mountain pass method; compactness level; ELLIPTIC-EQUATIONS; INEQUALITY;

D O I：

10.1007/s00009-023-02301-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a weighted fourth order equation involving a positive continuous potential in B. The non-linearity is assumed to have critical exponential growth in view of Adams' type inequalities. The weight w(x) is of logarithm type. It is proved that there is a nontrivial weak solution to this problem by the mountain Pass Theorem. We avoid the loss of compactness by proving a concentration compactness result and by a suitable asymptotic condition.

引用

页数：27

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