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

［1］ Adams R A,  Journier J. Sobolev Spaces［M］. Second edition.Amsterdam:Acad Press,2003.

［2］ Garcia Azorero J, Peral I, Rossi J D. A convexconcave problem with a nonlinear boundary condition［J］. J Differential Equations， 2004(198): 91-128.

［3］ Terraccini S. Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions［J］. Differential Integral Equations, 1995(8):1911-1922.

［4］ Ambrosetti A, Rabinowitz P. Dual variational methods in critical points theory and applications［J］. J Funct Anal,1973(14):349381.

［5］ Ekeland I. Nonvex minimization problems［J］. Bull Amer Math Soc, 1979(1): 443-473.

［6］ Li Shujie, Wu Shaoping,  Zhou Huansong. Solutions to semilinear elliptic problems with combined nonlinearities［J］. J Differential Equations, 2002(185):200-224.

［7］ Schechter M. A variation of the Mountain Pass lemma and applications［J］. J London Math Soc, 1991(44): 491-502.
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