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Semilinear elliptic Neumann problems with rapid growth in the nonlinearity

Published online by Cambridge University Press:  17 April 2009

Jason R. Looker
Jason R. Looker
Affiliation:
Particulate Fluids Processing Centre, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia e-mail: jrlooker@ms.unimelb.edu.au
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The existence and regularity of solutions to semilinear elliptic Neumann problems are investigated. Motivated by the Poisson–Boltzmann equation of biophysics and semiconductor modeling, the nonlinearity is assumed to be a continuous, strictly monotone increasing function that passes through the origin with asymptotically superlinear and unbounded growth. Pseudomonotone operator theory is utilised to establish the existence and uniqueness of a weak solution in the Sobolev space W1,2. With an additional assumption on the nonlinearity, we show that this weak solution belongs to .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 161 - 175
Copyright
Copyright © Australian Mathematical Society 2006

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