有扰动的（p，2）方程和拉普拉斯方程的非线性特征值问题

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-04-30 DOI:10.1007/s00025-024-02176-6

Krzysztof Bień

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引用次数: 0

摘要

我们考虑了涉及拉普拉斯和 p-Laplace 算子 \((p>2)\) 的两类非线性特征值问题。主要结果证明，在扰动方程的情况下，至少存在两个非难弱解，而在（p, 2）方程的情况下，存在连续谱。在这两种情况下，变分法在我们的论证中都发挥了核心作用。

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Nonlinear Eigenvalue Problems for (p, 2)-Equations and Laplace Equations with Perturbations

We consider two types of nonlinear eigenvalue problems involving Laplace and p-Laplace operators \((p>2)\). The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (p, 2)-equation. In both cases, variational methods play a central role in our arguments.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.