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
收藏
页码：81 / 86
页数：6
相关论文
共 47 条
[21]   Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations [J].
Xiaoling Han ;
Hongliang Gao .
Advances in Difference Equations, 2012
[22]   Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators [J].
Min-Jei Huang ;
Chao-Ya Huang ;
Tzong-Mo Tsai .
Mathematische Zeitschrift, 2007, 257 :581-595
[23]   MULTIPLE POSITIVE SOLUTIONS FOR A FOURTH-ORDER NONLINEAR EIGENVALUE PROBLEM [J].
Yong-Hui Zhou ;
Yun-Rui Yang ;
Li Liu .
AnnalsofAppliedMathematics, 2016, 32 (04) :418-428
[24]   Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations [J].
Han, Xiaoling ;
Gao, Hongliang .
ADVANCES IN DIFFERENCE EQUATIONS, 2012,
[25]   Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems [J].
Pacella F. .
Milan Journal of Mathematics, 2005, 73 (1) :221-236
[26]   Two-Parameter Eigenvalue Problems in Nonlinear Second Order Differential Equations [J].
Shibata T. .
Results in Mathematics, 1997, 31 (1-2) :136-147
[27]   Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter [J].
Simon Hilscher, Roman .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (12) :2922-2960
[28]   Positive solutions for a class of nonlinear parametric Robin problems [J].
Gasinski, Leszek ;
Papageorgiou, Nikolaos S. ;
Zhang, Youpei .
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2024, 73 (01) :429-454
[29]   Positive solutions for eigenvalue problems of fourth-order elastic beam equations [J].
Yao, QL .
APPLIED MATHEMATICS LETTERS, 2004, 17 (02) :237-243
[30]   Positive solutions for eigenvalue problems of fractional differential equations with p-Laplacian [J].
Lu, H. ;
Han, Z. ;
Sun, S. ;
Zhang, C. .
SCIENTIA IRANICA, 2015, 22 (03) :755-764
12345