Fixed point and variational methods for certain classes of boundary-value problems

被引:2
作者
O'Regan, Donal [1 ]
Orpel, Aleksandra [2 ]
机构
[1] Natl Univ Ireland, Dept Math, Galway, Ireland
[2] Univ Lodz, Fac Math & Comp Sci, PL-90131 Lodz, Poland
关键词
fixed point method; variational methods; positive solutions; variational principle; minimizing sequences; POSITIVE RADIAL SOLUTIONS; SEMILINEAR ELLIPTIC PROBLEMS; EXISTENCE; NONEXISTENCE; EQUATIONS;
D O I
10.1080/00036811.2012.678336
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article compares the topological and variational approaches for boundary-value problems. The main tools applied are Schauder's fixed point theorem and the variational approach based on the variational principle for minimizing sequences.
引用
收藏
页码:1393 / 1402
页数:10
相关论文
共 21 条
[1]  
BANDLE C, 1989, J REINE ANGEW MATH, V401, P25
[2]   NONLINEAR ELLIPTIC PROBLEMS IN ANNULAR DOMAINS [J].
BANDLE, C ;
COFFMAN, CV ;
MARCUS, M .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1987, 69 (03) :322-345
[3]   AN ODE APPROACH TO THE EXISTENCE OF POSITIVE SOLUTIONS FOR SEMI-LINEAR PROBLEMS IN RN [J].
BERESTYCKI, H ;
LIONS, PL ;
PELETIER, LA .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (01) :141-157
[4]  
BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
[5]   Positive solutions of a second-order singular ordinary differential equation [J].
Bonheure, D ;
Gomes, JM ;
Sanchez, L .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (08) :1383-1399
[6]   EXISTENCE AND NON-EXISTENCE RESULTS FOR SEMILINEAR ELLIPTIC PROBLEMS IN UNBOUNDED-DOMAINS [J].
ESTEBAN, MJ ;
LIONS, PL .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1982, 93 :1-14
[7]   Existence of multiple positive solutions of singular boundary value problems [J].
Ha, KS ;
Lee, YH .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (08) :1429-1438
[8]  
Lee YH, 2000, DIFFER INTEGRAL EQNS, V13, P31
[9]   POSITIVE RADIAL SOLUTIONS AND NONRADIAL BIFURCATION FOR SEMILINEAR ELLIPTIC-EQUATIONS IN ANNULAR DOMAINS [J].
LIN, SS .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 86 (02) :367-391
[10]   Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach [J].
Lue, Haishen ;
O'Regan, Donal ;
Agarwal, Ravi P. .
APPLICATIONS OF MATHEMATICS, 2007, 52 (02) :117-135