Electron. J. Diff. Eqns., Vol. 2007(2007), No. 160, pp. 1-9.

Resonant problem for some second-order differential equation on the half-line

Katarzyna Szymanska

We prove the existence of at least one solution to a nonlinear second-order differential equation on the half-line, with the boundary conditions x'(0)=0 and with the first derivative vanishing at infinity. Our main tool is the multi-valued version of the Miranda Theorem.

Submitted June 20, 2007. Published November 21, 2007.
Math Subject Classifications: 34B15, 34B40.
Key Words: Asymptotic boundary value problem; resonant problem; nonlinear boundary value problem; set-valued maps.

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Katarzyna Szymanska
Institute of Mathematics
Technical University of Lodz
90-924 Lodz, ul. Wolczanska 215, Poland
email: grampa@zb.net.lodz.pl

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