Transition between nonlinear and linear eigenvalue problems

被引：2

作者：

Jiang, Guosheng ^{[1
]}

Liu, Yongjie ^{[1
]}

Liu, Zhaoli ^{[2
]}

机构：

[1] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

[2] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Nonlinear eigenvalue problem; Linear eigenvalue problem; Transition; EQUATIONS;

D O I：

10.1016/j.jde.2020.07.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study convergence of variational solutions of the nonlinear eigenvalue problem -Delta u = lambda vertical bar u vertical bar(p-2)u, u is an element of H-0(1)(Omega), as p down arrow 2 or as p up arrow 2, where Omega is a bounded domain in R-N with smooth boundary. It turns out that if lambda is not an eigenvalue of -Delta then the solutions either blow up or vanish according to p down arrow 2 or p up arrow 2, while if is an eigenvalue of -Delta then the solutions converge to the associated eigenspace. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：10919 / 10936

页数：18

共 11 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2]

[Anonymous], 1997, Graduate Studies in Mathematics

[3] VARIANT OF LUSTERNIK-SCHNIRELMAN THEORY [J].

CLARK, DC .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1972, 22 (01) :65-&

[4] Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle [J].

Damascelli, L ;

Grossi, M ;

Pacella, F .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1999, 16 (05) :631-652

[5]

Gilbarg D., 2001, ELLIPTIC PARTIAL DIF

[6]

Han X, 2016, INT CONF CLOUD COMPU, P171, DOI 10.1109/CCIS.2016.7790247

[7] UNIQUENESS OF LEAST ENERGY SOLUTIONS TO A SEMILINEAR ELLIPTIC EQUATION IN R(2) [J].

LIN, CS .

MANUSCRIPTA MATHEMATICA, 1994, 84 (01) :13-19

[8] Schrodinger equations with concave and convex nonlinearities [J].

Liu, ZL ;

Wang, ZQ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2005, 56 (04) :609-629

[9]

Rabinowitz P.H., 1986, CBMS REG C SER MATH, V65

[10]

Stam A., 1959, Information and Control, V2, P101

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