Journal of Guangdong University of Technology ›› 2011, Vol. 28 ›› Issue (4): 30-33.

• Comprehensive Studies • Previous Articles     Next Articles

Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions

  

  1. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
  • Online:2011-12-25 Published:2011-12-25

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Abstract: It studies the existence of nontrivial solutions to an asymptotically linear elliptic problem with nonlinear boundary conditions on Ω，where Ω is a bounded smooth domain in RN(N≥3), and the nonlinear term f(x,u) is asymptotically linear with respect to u at infinity. By Ekeland’s variational principle and a variant version of Mountain Pass Theorem, it proves that there exist at least two nontrivial solutions if the nonnegative parameter SymbollA is small enough.

Key words: asymptotically linear; nonlinear boundary conditions; Mountain Pass Theorem

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