Positive solutions of superlinear boundary value problems with singular indefinite weight

被引：14

作者：

Gaudenzi, M

Habets, P

Zanolin, F

机构：

[1] Inst Math Pures & Appl, B-1348 Louvain, Belgium

[2] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2003年 / 2卷 / 03期

关键词：

positive solutions; superlinear equations; indefinite weight; singular coefficients;

D O I：

10.3934/cpaa.2003.2.411

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we propose a method to deal with non-ordered lower and upper solutions in the case of ODE's with singular coefficients. As an application, we study the existence of positive solutions for a two-point boundary value problem on]0, 1[ associated to the equation u" + a(t)g(u) = 0, where the function g : R+ --> R+ is continuous with superlinear growth at infinity and the weight a(t) changes sign as well as it may present some singularities at t = 0 or t = 1.

引用

页码：411 / 423

页数：13

共 15 条

[1] Elliptic problems with nonlinearities indefinite in sign [J].

Alama, S ;

Tarantello, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 141 (01) :159-215

[2] ELLIPTIC EQUATIONS WITH NON-INVERTIBLE FREDHOLM LINEAR PART AND BOUNDED NONLINEARITIES [J].

AMANN, H ;

AMBROSETTI, A ;

MANCINI, G .

MATHEMATISCHE ZEITSCHRIFT, 1978, 158 (02) :179-194

[3] A priori bounds and multiple solutions for superlinear indefinite elliptic problems [J].

Amann, H ;

Lopez-Gomez, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 146 (02) :336-374

[4]

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

[5]

Berestycki H., 1995, Nonlinear Differ Equ Appl, V2, P553, DOI [DOI 10.1007/BF01210623, 10.1007/BF01210623]

[6]

Berestycki H., 1994, Topol. Methods Nonlinear Anal, V4, P59, DOI [10.12775/TMNA.1994.023, DOI 10.12775/TMNA.1994.023]

[7]

Brezis H., 1977, Comm. Part. Differ. Equ, V2, P601, DOI DOI 10.1080/03605307708820041

[8] Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order [J].

De Coster, C ;

Henrard, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (02) :420-452

[9]

de Coster C., 1993, CISM COURSES LECT, V371, P1

[10]

DECOSTER C, 1995, APPL ANAL, V59

← 1 2 →