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Journal of the London Mathematical Society 1998 58(3):733-747; doi:10.1112/S0024610798006784
© 1998 by London Mathematical Society
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© The London Mathematical Society

Bounded Solutions of Some Second Order Nonlinear Differential Equations

Jean Mawhin and James R. Ward

Institut Mathématique, Université de Louvain B-1348 Louvain-la-Neuve, Belgium
Department of Mathematics, University of Alabama Birmingham, Alabama 35294, USA

Received 25 November 1995.

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.


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