Fifth Mississippi State Conference on Differential Equations and
Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 143152.
A nonresonant multipoint boundaryvalue problem for a pLaplacian
type operator
Chaitan P. Gupta
Abstract:
Let
be an odd increasing homeomorphism from
onto
with
,
,
be a
function satisfying Caratheodory's conditions and
.
Let
,
,
,
,
be given.
This paper is concerned with the problem of existence of a solution for
the multipoint boundaryvalue problem
This paper gives conditions for the existence of a solution for
the above boundaryvalue problem using some new Poincare type
a priori estimates. In the case
for
,
this problem was studied earlier by Gupta, Trofimchuk in
[2] and by Gupta, Ntouyas and Tsamatos in [1]. We
give a priori estimates needed for this problem
that are similar to a priori estimates obtained by Gupta, Trofimchuk in
[2]. We then obtain existence theorems for the above multipoint
boundaryvalue problem using the a priori estimates and
LeraySchauder continuation theorem.
Published February 28, 2003.
Subject classifications: 34B10, 34B15, 34G20.
Key words: Multipoint boundaryvalue problem, threepoint boundaryvalue problem,
pLaplacian, Leray Schauder Continuation theorem,
Caratheodory's conditions.
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Chaitan P. Gupta
Department of Mathematics, 084
University of Nevada, Reno
Reno, NV 89557, USA
email: gupta@unr.edu 
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