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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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

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

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