Branches of positive solutions of subcritical elliptic equations in convex domains

Alfonso Castro; Rosa  Pardo

doi:10.3934/proc.2015.0230

Article Contents

2015, Volume 2015: 230-238. Doi: 10.3934/proc.2015.0230 open access

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Branches of positive solutions of subcritical elliptic equations in convex domains

Alfonso Castro^1, and
Rosa Pardo^2,

1.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711
2.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040-Madrid

Received: September 2014

Revised: March 2015

Published: November 2015

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Abstract

We provide sufficient conditions for the existence of $L^{\infty}$ a priori estimates for positive solutions to a class of subcritical elliptic equations in bounded $C^2$ convex domains. These sufficient conditions widen the range of nonlinearities for which a priori bounds are known. Using these a priori bounds we prove the existence of positive solutions for a class of problems depending on a parameter

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Mathematics Subject Classification: Primary: 35B45; Secondary: 35B09, 35B33, 35J25, 35J60.

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References

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