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BOUNDED SOLUTIONS OF SOME SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  01 December 1998

JEAN MAWHIN  and
JAMES R. WARD
JEAN MAWHIN
Affiliation:
Institut Mathématique, Université de Louvain, B-1348 Louvain-la-Neuve, Belgium
JAMES R. WARD
Affiliation:
Department of Mathematics, University of Alabama, Birmingham, Alabama 35294, USA
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Abstract

We prove Landesman–Lazer type existence conditions for the solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equations of the form x″+cx′+f(t, x)=0. The proofs use upper and lower solutions techniques together with some limiting arguments.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 733 - 747
Copyright
The London Mathematical Society 1998

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