Seventh Mississippi State  UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 17 (2009), pp. 8194.
A thirdorder mpoint boundaryvalue problem of Dirichlet type
involving a pLaplacian type operator
Chaitan P. Gupta
Abstract:
Let
, be an odd increasing homeomorphisms from
onto
satisfying
, and let
be a
function satisfying Caratheodory's conditions.
Let
,
,
,
be given. We are interested in the
existence of solutions for the
point
boundaryvalue problem:
in the resonance and nonresonance cases. We say that this problem is at
\emph{resonance} if the associated problem
with the above boundary conditions has a nontrivial solution.
This is the case if and only if
.
Our results use topological degree
methods. In the nonresonance case; i.e., when
we note that the sign of
degree for the relevant operator depends on the sign of
.
Published April 15, 2009.
Math Subject Classifications: 34B10, 34B15, 34L30.
Key Words: mpoint boundary value problems; pLaplace type operator;
nonresonance; resonance; topological degree.
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Chaitan P. Gupta
Department of Mathematics, 084
University of Nevada
Reno, NV 89557, USA
email: gupta@unr.edu 
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