Abstract and Applied Analysis

Multiplicity of Solutions to a Potential Operator Equation and Its Applications

Jincheng Huang

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We consider the multiplicity of solutions for operator equation involving homogeneous potential operators. With the help of Nehari manifold and fibering maps, we prove that such equation has at least two nontrivial solutions. Furthermore, we apply this result to prove the existence of two nonnegative solutions for three types of quasilinear elliptic systems involving (p, q)-Laplacian operator and concave-convex nonlinearities.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 947139, 11 pages.

First available in Project Euclid: 27 February 2015

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Huang, Jincheng. Multiplicity of Solutions to a Potential Operator Equation and Its Applications. Abstr. Appl. Anal. 2014 (2014), Article ID 947139, 11 pages. doi:10.1155/2014/947139. https://projecteuclid.org/euclid.aaa/1425049848

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