Differential and Integral Equations

A fibering map approach to a potential operator equation and its applications

Kenneth J. Brown and Tsung-Fang Wu

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In this paper, we study the existence of multiple solutions for operator equations involving homogeneous potential operators. With the help of the Nehari manifold and the fibering method, we prove that some such equations have at least two nonzero solutions. Furthermore, we apply this result to prove the existence of two positive solutions for some quasilinear elliptic problems involving sign-changing weight functions.

Article information

Differential Integral Equations, Volume 22, Number 11/12 (2009), 1097-1114.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]


Brown, Kenneth J.; Wu, Tsung-Fang. A fibering map approach to a potential operator equation and its applications. Differential Integral Equations 22 (2009), no. 11/12, 1097--1114. https://projecteuclid.org/euclid.die/1356019406

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