Differential and Integral Equations

A three critical points result in a bounded domain of a Banach space and applications

Radu Precup, Patrizia Pucci, and Csaba Varga

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Abstract

Using the bounded mountain pass lemma and the Ekeland variational principle, we prove a bounded version of the Pucci-Serrin three critical points result in the intersection of a ball with a wedge in a Banach space. The localization constraints are overcome by boundary and invariance conditions. The result is applied to obtain multiple positive solutions for some semilinear problems.

Article information

Source
Differential Integral Equations, Volume 30, Number 7/8 (2017), 555-568.

Dates
Accepted: August 2016
First available in Project Euclid: 4 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1493863394

Mathematical Reviews number (MathSciNet)
MR3646463

Zentralblatt MATH identifier
06738561

Subjects
Primary: 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 34B15: Nonlinear boundary value problems

Citation

Precup, Radu; Pucci, Patrizia; Varga, Csaba. A three critical points result in a bounded domain of a Banach space and applications. Differential Integral Equations 30 (2017), no. 7/8, 555--568. https://projecteuclid.org/euclid.die/1493863394


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