Opuscula Math. 33, no. 4 (2013), 713-723

Opuscula Mathematica

Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation

Ryuji Kajikiya

Abstract. We study the sublinear Emden-Fowler equation in small domains. As the domain becomes smaller, so does any solution. We investigate the convergence rate of the Sobolev norm of solutions as the volume of the domain converges to zero. The result is obtained by estimating the first eigenvalue of the Laplacian with the help of the variational method.

Keywords: Emden-Fowler equation, sign-changing solution, positive solution, variational method, norm estimate.

Mathematics Subject Classification: 35J20, 35J25.

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  • Ryuji Kajikiya
  • Saga University, Faculty of Science and Engineering, Department of Mathematics, Saga, 840-8502, Japan
  • Received: 2013-02-18.
  • Accepted: 2013-04-10.
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Cite this article as:
Ryuji Kajikiya, Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation, Opuscula Math. 33, no. 4 (2013), 713-723, http://dx.doi.org/10.7494/OpMath.2013.33.4.713

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