1999
DOI: 10.1006/jfan.1999.3446
|View full text |Cite
|
Sign up to set email alerts
|

Positive Solutions of Superlinear Elliptic Equations

Abstract: In this paper, we study the existence of two positive solutions of superlinear elliptic equations without assuming the conditions which have been used in the literature to deduce either the P.S. condition or a priori bounds of positive solutions. The first solution is proved as the minimal positive solution, while the second one is obtained as the limit of a gradient flow whose starting point is properly chosen. The dependence of the minimal solution upon a parameter is also considered. Academic Press

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
19
0

Year Published

2000
2000
2015
2015

Publication Types

Select...
8

Relationship

2
6

Authors

Journals

citations
Cited by 33 publications
(19 citation statements)
references
References 22 publications
0
19
0
Order By: Relevance
“…The proof follows the line of [11, Proposition IV-3.1] together with a bootstrap argument that can be found for example in [21].…”
Section: Proposition 33 Let Assumptions (H) Be Satisfied and U(t; Umentioning
confidence: 80%
See 1 more Smart Citation
“…The proof follows the line of [11, Proposition IV-3.1] together with a bootstrap argument that can be found for example in [21].…”
Section: Proposition 33 Let Assumptions (H) Be Satisfied and U(t; Umentioning
confidence: 80%
“…The first part of the result can be proved as in [11,. The second part is proved following the ideas of [11, Theorem IV-3.5] together with a bootstrap argument that can be found for example in [21].…”
Section: If Moreover the Palais-smale Condition (Ps) Is Satisfied Thmentioning
confidence: 99%
“…Note that Lemma 2.1 was proved in [3] only for the Dirichlet boundary condition, but the same proof works very well for the Neumann boundary condition. This remark is suitable for all the lemmas in the sequel which are quoted from literature.…”
Section: Lemma 21 ([3 Lemma 2 and 5]) Assume Thatmentioning
confidence: 99%
“…Positive solutions of nonlinear elliptic problems on a bounded domain have been much studied (see, for example [3,10,11,12]). But to our best knowledge, it seems that there few results about (1.1) which is a p-laplacian equation with nonlinearity asymptotic to…”
Section: Introductionmentioning
confidence: 99%