Existence and Multiplicity of Solutions for a Class of Kirchhoff-Boussinesq-Type Problems with Logarithmic Growth

被引：3

作者：

Carlos, Romulo D. ^{[1
]}

Mbarki, Lamine ^{[2
]}

Yang, Shuang ^{[3
]}

机构：

[1] Univ Brasilia UnB, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Univ Tunis El Manar, Fac Sci Tunis, Math Dept, Tunis 2092, Tunisia

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 03期

关键词：

Kirchhoff-Boussinesq; Nehari manifold; logarithmic growth; variational methods; mountain pass theorem; NONLINEAR SCHRODINGER-EQUATIONS; GROUND-STATE SOLUTION; NONTRIVIAL SOLUTIONS; P-LAPLACIAN; BIHARMONIC-EQUATIONS; BEHAVIOR;

D O I：

10.1007/s00009-024-02649-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, two problems related to the following class ofelliptic Kirchhoff-Boussinesq-type models are analyzed in the subcritical(beta= 0) and critical (beta= 1) cases: Delta(2)u-Delta(p)u=tau|u|(q-2)uln|u|+beta|u|(2)& lowast;& lowast;(-2)u in Omega and Delta u=u=0 on partial derivative Omega, where tau > 0, 2 < p < 2 & lowast; = 2N/N-2 for N >= 3 and 2(& lowast;& lowast; )= infinity for N = 3, N = 4, 2(& lowast;& lowast; )= 2N/N-4 for N >= 5. The first one is concerned with the existence of a nontrivial ground-state solution via variational methods. As for the second problem, we prove the multiplicity of such a solution using the Mountain Pass Theorem.

引用

页数：26

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