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

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