Petio Kelevedjiev, Panos K. Palamides, Nedyu Popivanov
Abstract:
In this article we investigate the existence of positive and/or negative
solutions of a classes of four-point boundary-value problems for
fourth-order ordinary differential equations. The assumptions in this
article are more relaxed than the known assumptions. Our technique relies on
the continuum property (connectedness and compactness) of the solutions
funnel (Knesser's Theorem), combined with the corresponding vector field's
ones. This approach permits the extension of results (getting positive
solutions) to nonlinear boundary conditions, whenever the corresponding
Green's kernel is not of definite sign or there does not exist (see the last
Corollary).
Submitted February 5, 2008. Published March 30, 2008.
Math Subject Classifications: 34B15, 34B25.
Key Words: Multipoint boundary value problem; positive solution;
vector field; third order differential equation;
Green function; Krasnoselskii's fixed point theorem.
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Petio S. Kelevedjiev Department of Mathematics Technical University of Sliven 8800 Sliven, Bulgaria e-mail: keleved@mailcity.com |
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Panos K. Palamides Naval Academy of Greece Piraeus, 451 10, Greece email: ppalam@otenet.gr ppalam@snd.edu.gr http://ux.snd.edu.gr/~maths-ii/pagepala.htm |
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Nedyu I. Popivanov Faculty of Mathematics and Informatics "St. Kl. Ohridski" University of Sofia 1164 Sofia, Bulgaria email: nedyu@fmi.uni-sofia.bg |
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