Nonuniform nonresonance for nonlinear boundary value problems with y′ dependence

Abstract

A new nonuniform nonresonant result at the first eigenvalue is presented for the boundary value problem \(\ y^{\prime \prime}+q\ f\left( t,y,y^{\prime}\right) =0\) a.e.on \(\left[ 0,1\right] ,y\left( 0\right) =y\left(1\right) =0\).

Authors

Ravi P. Agarwal
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901–6975

Donal O’Regan
Department of Mathematics, National University of Ireland, Galway, Ireland

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Nonuniform nonresonant; boundary value problem; eigenvalues; eigen-functions.

Paper coordinates

R. Precup, R.P. Agarwal, D. O’Regan, Nonuniform nonresonance for nonlinear boundary value problems with y′ dependence, Dynamic Systems Appl. 16 (3) (2007), 587-594.

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About this paper

Journal

Dynamic Systems and Applications

Publisher Name
DOI

Print ISSN
Online ISSN

1056-2176

google scholar link

[1] R.P. Agarwal, D. O’Regan and V. Lakshmikantham, Quadratic forms and nonlinear nonresonant singular second order boundary value problems of limit circle type, Zeitschrift fur Analysis und ihre Anwendungen 20(2001), 727–737.
[2] A. Granas, R.G. Guenther and J.W. Lee, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pures Appl. 70(1991), 153–196.
[3] J. Mawhin and J.R. Ward, Nonuniform nonresonance conditions at the first two eigenvalues for periodic solutions of forced Lienard and Duffing equations, Rocky M. J. Math. 12(1982), 643–654.
[4] D. O’Regan, Theory of Singular Boundary Value Problems, World Scientific, Singapore, 1994.
[5] D. O’Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer, Dordrecht, 1997.

2007

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