具有指数增长非线性的加权四阶薛定谔方程的基态解

IF 0.5 4区数学 Q3 MATHEMATICS

Lithuanian Mathematical Journal Pub Date : 2024-01-06 DOI:10.1007/s10986-023-09617-9

Rima Chetouane, Brahim Dridi, Rached Jaidane

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引用次数: 0

摘要

在本文中，我们确定了在ℝ4 的单位球 B 中边界狄利克特条件下薛定谔型加权四阶方程的基态解的存在性。由于亚当斯型不等式与多项式项相结合，方程的非线性假定为指数增长。我们使用了 Nehari 集合中的约束最小化、定量变形 Lemma 和度理论结果。

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Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity

In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet condition in the unit ball B of ℝ⁴. The potential V is a continuous positive function bounded away from zero in B. The nonlinearity of the equation is assumed to have exponential growth due to Adams-type inequalities combined with polynomial term. We use the constrained minimization in the Nehari set, the quantitative deformation lemma, and degree theory results.

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来源期刊

Lithuanian Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics. The scope of the journal includes but is not limited to: Probability theory and statistics; Differential equations (theory and numerical methods); Number theory; Financial and actuarial mathematics, econometrics.