Differential and Integral Equations

A variant of mountain pass theorem

Gabriele Bonanno and Giuseppina D'Aguì

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An existence result for a critical point of mountain-pass type, where the classical Palais--Smale condition is not required, is presented. A multiple-critical-point result is then obtained. As an application, the existence of two positive classical solutions for two-point boundary-value problems, without assuming any asymptotic condition on the nonlinearity, is obtained.

Article information

Differential Integral Equations, Volume 26, Number 9/10 (2013), 1149-1156.

First available in Project Euclid: 3 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35J20: Variational methods for second-order elliptic equations 49J35: Minimax problems 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]


Bonanno, Gabriele; D'Aguì, Giuseppina. A variant of mountain pass theorem. Differential Integral Equations 26 (2013), no. 9/10, 1149--1156. https://projecteuclid.org/euclid.die/1372858568

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