Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 647-669, 2007

On the existence and the stability of solutions for
higher-order semilinear Dirichlet problems

M. Galewski, M. Plocienniczak

Marek Galewski, Marek Plocienniczak, Faculty of Mathematics, University of Lodz, Banacha 22, 90-238 Lodz, Poland, e-mails: galewski@math.uni.lodz.pl, plo@math.uni.lodz.pl

Abstract: We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.

Keywords: Dirichlet problem

Classification (MSC 2000): 35J20


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