Abstract and Applied Analysis

Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components

Luisa Toscano and Speranza Toscano

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Abstract

We study the solvability of Dirichlet and Neumann problems for different classes of nonlinear elliptic systems depending on parameters and with nonmonotone operators, using existence theorems related to a general system of variational equations in a reflexive Banach space. We also point out some regularity properties and the sign of the found solutions components. We often prove the existence of at least two different solutions with positive components.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 760854, 44 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365125168

Digital Object Identifier
doi:10.1155/2012/760854

Mathematical Reviews number (MathSciNet)
MR2959763

Zentralblatt MATH identifier
1250.35095

Citation

Toscano, Luisa; Toscano, Speranza. Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 760854, 44 pages. doi:10.1155/2012/760854. https://projecteuclid.org/euclid.aaa/1365125168


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References

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