Seventh Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 17 (2009), pp. 207-212.
Existence and nonexistence results for quasilinear
semipositone Dirichlet problems
Matthew Rudd
Abstract:
We use the sub/supersolution method to analyze a semipositone Dirichlet
problem for the p-Laplacian. To find a positive solution, we therefore
focus on a related problem that produces positive subsolutions.
We establish a new nonexistence result for this subsolution problem on
general domains, discuss the existence of positive radial subsolutions
on balls, and then apply our results to problems involving particular
semipositone nonlinearities.
Published April 15, 2009.
Math Subject Classifications: 34B10, 35J20.
Key Words: semipositone problems; p-Laplacian; positive solutions.
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Matthew Rudd
Department of Mathematics
University of Idaho
Moscow, ID 83844, USA
email: mrudd@uidaho.edu |
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