On the nonlinear perturbations of self-adjoint operators

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI:10.1515/anona-2022-0235

Michal Beldzinski, M. Galewski, Witold Majdak

引用次数: 1

Abstract

Abstract Using elements of the theory of linear operators in Hilbert spaces and monotonicity tools we obtain the existence and uniqueness results for a wide class of nonlinear problems driven by the equation T x = N ( x ) Tx=N\left(x) , where T T is a self-adjoint operator in a real Hilbert space ℋ {\mathcal{ {\mathcal H} }} and N N is a nonlinear perturbation. Both potential and nonpotential perturbations are considered. This approach is an extension of the results known for elliptic operators.

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关于自伴随算子的非线性扰动

摘要利用Hilbert空间线性算子理论的元素和单调性工具，得到了一类由方程Tx=N (x) Tx=N\left(x)驱动的非线性问题的存在唯一性结果，其中T T是实Hilbert空间H {\mathcal{{\mathcal H}}}中的自伴随算子，N N是非线性摄动。考虑了势和非势扰动。这种方法是对椭圆算子已知结果的扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.