Existence of three solutions for a quasilinear two point boundary value problem

Livrea, Roberto

doi:10.1007/s00013-002-8315-0

Cited by 39 publications

(15 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also refer the reader to the papers [26,28,29] where the existence of infinitely many solutions for some boundary value problems has been studied by using different approaches.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Infinitely Many Solutions for a Perturbed Quasilinear Two-Point Boundary Value Problem

Heidarkhani¹,

Henderson²

2014

Annals of the Alexandru Ioan Cuza University - Mathematics

View full text Add to dashboard Cite

Abstract. In this paper we deal with the existence of infinitely many weak solutions for a perturbed quasilinear two-point boundary value problem. More precisely the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.Mathematics Subject Classification 2010: 47J10, 34B15.

show abstract

“…We also refer the reader to the papers [26,28,29] where the existence of infinitely many solutions for some boundary value problems has been studied by using different approaches.…”

Section: Introductionmentioning

confidence: 99%

“…For other basic notations and definitions, and for a thorough account on the subject, we refer the reader to [1,2,5,12,16,17,20,22,23,24,26,32].…”

Section: Introductionmentioning

confidence: 99%

Infinitely Many Solutions for a Perturbed Quasilinear Two-Point Boundary Value Problem

Heidarkhani¹,

Henderson²

2014

Annals of the Alexandru Ioan Cuza University - Mathematics

View full text Add to dashboard Cite

show abstract

“…Under further assumptions, this fact leads to a three critical points theorem (see [13,Theorem 1] improving [12,Theorem 3.1]) which has been widely applied to get multiplicity results for nonlinear boundary value problems [1,2,3,5,6,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Further results related to a minimax problem of Ricceri

Cordaro

2005

J Inequal Appl

View full text Add to dashboard Cite

We deal with a theoric question raised in connection with the application of a threecritical points theorem, obtained by Ricceri, which has been already applied to obtain multiplicity results for boundary value problems in several recent papers. In the settings of the mentioned theorem, the typical assumption is that the following minimax inequalityhas to be satisfied by some continuous and concave function h : I → R. When I = [0,+∞[, we have already proved, in a precedent paper, that the problem of finding such function h is equivalent to looking for a linear one. Here, we consider the question for any interval I and prove that the same conclusion holds. It is worth noticing that our main result implicitly gives the most general conditions under which the minimax inequality occurs for some linear function. We finally want to stress out that although we employ some ideas similar to the ones developed for the case where I = [0,+∞[, a key technical lemma needs different methods to be proved, since the approach used for that particular case does not work for upper-bounded intervals.

show abstract

“…For a thorough account on the subject, we refer to [1,3,4,[6][7][8][9][10]12] and the references therein.…”

mentioning

confidence: 99%

Multiplicity results for a two-point boundary value double eigenvalue problem

Afrouzi

Heidarkhani

2010

Ricerche mat.

View full text Add to dashboard Cite

show abstract

Existence of three solutions for a quasilinear two point boundary value problem

Abstract: In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:Our main tool is a recent three critical points theorem of B. Ricceri ([10]).

Cited by 39 publications

References 11 publications

Infinitely Many Solutions for a Perturbed Quasilinear Two-Point Boundary Value Problem

Infinitely Many Solutions for a Perturbed Quasilinear Two-Point Boundary Value Problem

Further results related to a minimax problem of Ricceri

Multiplicity results for a two-point boundary value double eigenvalue problem

Contact Info

Product

Resources

About