Semilinear elliptic equations with generalized cubic nonlinearities

Junping Shi; R. Shivaji

doi:10.3934/proc.2005.2005.798

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2005, Volume 2005: 798-805. Doi: 10.3934/proc.2005.2005.798 open access

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Semilinear elliptic equations with generalized cubic nonlinearities

Junping Shi^1, and
R. Shivaji^2,

1.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
2.
Department of Mathematics and Statistics, Center for Computational Sciences, Mississippi State University, Mississippi State, MS 39762

Received: August 31, 2004

Revised: March 31, 2005

Published: August 2005

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Abstract

A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.

Keywords:

semilinear reaction-diffusion equation,
global bifurcation.

Mathematics Subject Classification: Primary: 35J65, Secondary: 35B32, 92D25, 92D40.

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