Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE MULTIPLE POSITIVE SOLUTIONS TO A QUASILINEAR EQUATION

  • Sang Don Park (Department of Mathematics, Yonsei University, Seoul 120-749, Korea) ;
  • Soo Hyun Bae (Department of Mathematics, Yonsei University, Seoul 120-749, Korea) ;
  • Dae Hyeon Pahk (Department of Mathematics, National Ansung industry University, Kyunggido 456-749, Korea)
  • Published : 1997.04.01
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Abstract

In this paper we investigate the multiplicity of positive solutions to a quasilinear Neumann problem; $$ {\varepsilon^m div($\mid$\bigtriangledown_u$\mid$^{m-2}\bigtriangledown_u) - u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{p-2} = 0 in \omega $$ $$ \frac{\partial u}{\partial \nu} = 0 on \partial \omega, $$ making use of Ljusternik Schnirelmann category theory.

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