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Solvability of semilinear abstract equations at resonance

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

Zachariah Sinkala
Zachariah Sinkala
Affiliation:
Department of Mathematics & Statistics, Middle Tennessee State University, Murfreesboro, TN 37132, U.S.A.
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Abstract

We establish a generalization of the Cesari-Kannan existence result for problems of the type Lx = N(x), x∈X where X is a separable Hilbert functional space, L is a selfadjoint linear differential operator with nontrivial finite dimensional kernel and N:X→X is a bounded continuous nonlinear operator. This generalization leads to new results when the dimension of the kernel of L is greater than one. Applications to systems of second order ordinary differential equations are given.

MSC classification

Secondary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 301 - 311
Copyright
Copyright © University College London 1994

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References

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