MATHEMATICA BOHEMICA, Vol. 135, No. 2, pp. 113-121, 2010

A third order boundary value problem subject to nonlinear boundary conditions

Gennaro Infante, Paolamaria Pietramala

G. Infante, Dipartimento di Matematica, Universita della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy, e-mail: g.infante@unical.it; P. Pietramala, Dipartimento di Matematica, Universita della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy, e-mail: pietramala@unical.it

Abstract: Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.

Keywords: positive solution, nonlinear boundary conditions, third order problem, cone, fixed point index

Classification (MSC 2010): 34B18, 34B10, 47H10, 47H30

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