On a Liouville-type equation with sign-changing weight

被引：1

作者：

Ruf, Bernhard ^{[1
]}

Ubilla, Pedro ^{[2
]}

机构：

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Santiago Chile, Dept Matemat & CC, Santiago, Chile

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2009年 / 139卷

关键词：

2-DIMENSIONAL EULER EQUATIONS; STATISTICAL-MECHANICS; LOCAL SUPERLINEARITY; STATIONARY FLOWS; EXISTENCE; BLOW;

D O I：

10.1017/S0308210507000583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems -Delta u = lambda(a(x)eu + f(x, u)), u is an element of H-0(1) (Omega), where Omega is a bounded domain in R-2 and lambda > 0 is a parameter. The coefficient a(x) is permitted to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the Trudinger-Moser inequality and variational methods. Note that when f(x, u) = 0 the equation is of Liouville type.

引用

页码：183 / 192

页数：10

共 50 条

[11] The Calogero Equation and Liouville-Type Equations
M. V. Pavlov
Theoretical and Mathematical Physics, 2001, 128 : 927 - 932
[12] Existence of solutions for a semilinear elliptic equation in RN with sign-changing weight
Yang, Jianfu
Yu, Xiaohui
ADVANCED NONLINEAR STUDIES, 2008, 8 (02) : 401 - 412
[13] FOR BIHARMONIC CRITICAL CHOQUARD EQUATION INVOLVING SIGN-CHANGING WEIGHT FUNCTIONS
Rani, Anu
Goyal, Sarika
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2022, 59 (01) : 221 - 260
[14] The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function
Brown, KJ
Zhang, YP
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) : 481 - 499
[15] The ∞-eigenvalue problem with a sign-changing weight
Kaufmann, Uriel
Rossi, Julio D.
Terra, Joana
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2019, 26 (02):
[16] A Kirchhoff-type equation involving critical exponent and sign-changing weight functions in dimension four
Lou, Qing-Jun
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (13) : 5159 - 5177
[17] EIGENVALUES OF DISCRETE STURM-LIOUVILLE PROBLEMS WITH SIGN-CHANGING WEIGHT AND COUPLED BOUNDARY CONDITIONS
Gao, Chenghua
Zhang, Fei
Ran, Maojun
OPERATORS AND MATRICES, 2020, 14 (02): : 491 - 513
[18] Existence of multiple solutions of Kirchhoff type equation with sign-changing potential
Zhang, Jian
Tang, Xianhua
Zhang, Wen
APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 : 491 - 499
[19] Positive solutions of the periodic problems for quasilinear difference equation with sign-changing weight
Man Xu
Ruyun Ma
Zhiqian He
Advances in Difference Equations, 2018
[20] Positive solutions of the periodic problems for quasilinear difference equation with sign-changing weight
Xu, Man
Ma, Ruyun
He, Zhiqian
ADVANCES IN DIFFERENCE EQUATIONS, 2018,

← 1 2 3 4 5 →