TRIPLE SOLUTIONS FOR QUASILINEAR ONE-DIMENSIONAL p-LAPLACIAN ELLIPTIC EQUATIONS IN THE WHOLE SPACE

被引：7

作者：

Bonanno, Gabriele ^{[1
]}

O'Regan, Donal ^{[2
]}

Vetro, Francesca ^{[3
]}

机构：

[1] Univ Messina, Dept Engn, I-98166 Messina, Italy

[2] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[3] Univ Palermo, Dept Energy Informat Engn & Math Models DEIM, Viale Sci Ed 8, I-90128 Palermo, Italy

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2017年 / 8卷 / 02期

关键词：

nonlinear differential problems in unbounded domains; operators without compactness; critical points; three solutions; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS; SCHRODINGER-EQUATIONS; INTERVALS; THEOREM;

D O I：

10.1215/20088752-0000010X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais-Smale condition, is exploited.

引用

页码：248 / 258

页数：11

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