A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function

K. J. Brown; Tsung Fang Wu

doi:10.1016/j.jmaa.2007.04.064

A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function

K. J. Brown, Tsung Fang Wu

Research output: Contribution to journal › Article › peer-review

82 Citations (Scopus)

Abstract

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (E_{?, µ}) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (?, µ) belongs to a certain subset of R². © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	1326-1336
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	337
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2007.04.064
Publication status	Published - 15 Jan 2008

Keywords

Nehari manifold
Nonlinear boundary conditions
Semilinear elliptic systems

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10.1016/j.jmaa.2007.04.064

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abstract = "In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (E?, µ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (?, µ) belongs to a certain subset of R2. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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AB - In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (E?, µ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (?, µ) belongs to a certain subset of R2. © 2007 Elsevier Inc. All rights reserved.

KW - Nehari manifold

KW - Nonlinear boundary conditions

KW - Semilinear elliptic systems

U2 - 10.1016/j.jmaa.2007.04.064

DO - 10.1016/j.jmaa.2007.04.064

M3 - Article

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VL - 337

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EP - 1336

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function

Abstract

Keywords

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