Approximation of Positive Solutions to Symmetric Eigenvalue Problems with Nonlinear Dependence on the Spectral Parameter

被引：0

作者：

Solov'ev, P. S. ^{[1
]}

机构：

[1] Kazan Fed Univ, Kazan 420008, Russia

来源：

RUSSIAN MATHEMATICS | 2024年 / 68卷 / 08期

关键词：

eigenvalue; positive eigenfunction; eigenvalue problem; finite element method; FINITE-ELEMENT APPROXIMATION; MINIMAL EIGENVALUE;

D O I：

10.3103/S1066369X24700725

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A symmetric partial differential eigenvalue problem with nonlinear dependence on the spectral parameter arising in plasma physics is studied. New conditions for the existence of a positive eigenvalue and the corresponding positive eigenfunctions are proposed and justified. A finite element approximation for the problem preserving the property of positivity of solutions is constructed. The existence and convergence of approximate solutions are established.

引用

页码：81 / 86

页数：6

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