Chan-Gyun Kim, Junping Shi
Abstract:
A p-Laplacian boundary-value problem with positive nonlinearity
is considered. The existence of a continuum of positive solutions
emanating from
is shown, and it can be extended
to
.
Under an additional condition on the nonlinearity,
it is shown that the positive solution is unique for any
;
thus the continuum
is indeed a continuous curve globally
defined for all
.
In addition, by the upper and lower solutions
method, existence of three positive solutions is established under some
conditions on the nonlinearity.
Submitted May 25, 2012. Published June 25, 2012.
Math Subject Classifications: 34B18, 34C23, 35J25.
Key Words: Upper and lower solution; positive solution;
p-Laplacian; uniqueness; multiplicity.
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Chan-Gyun Kim Department of Mathematics, College of William and Mary Williamsburg, Virginia 23187-8795, USA email: cgkim75@gmail.com | |
Junping Shi Department of Mathematics, College of William and Mary Williamsburg, Virginia 23187-8795, USA. School of Mathematical Sciences, Shanxi University Taiyuan, Shanxi 030006, China email: shij@math.wm.edu |
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