A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function |
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| Authors: | K.J. Brown |
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| Affiliation: | a Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK
b Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan |
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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 (Eλ,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 (λ,μ) belongs to a certain subset of R2. |
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| Keywords: | Semilinear elliptic systems Nonlinear boundary conditions Nehari manifold |
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