Differential and Integral Equations
- Differential Integral Equations
- Volume 30, Number 7/8 (2017), 555-568.
A three critical points result in a bounded domain of a Banach space and applications
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.
Differential Integral Equations, Volume 30, Number 7/8 (2017), 555-568.
Accepted: August 2016
First available in Project Euclid: 4 May 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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