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Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos — 2004

Annales Polonici Mathematici

We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

G. L. KarakostasP. Ch. Tsamatos — 2002

Annales Polonici Mathematici

We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.

Multiple positive solutions for a second order delay boundary value problem on the half-line

K. G. MavridisCh. G. PhilosP. Ch. Tsamatos — 2006

Annales Polonici Mathematici

Second order nonlinear delay differential equations are considered, and Krasnosel'skiĭ's fixed point theorem is used to establish a result on the existence of positive solutions of a boundary value problem on the half-line. This result can be used to guarantee the existence of multiple positive solutions. A specification of the result obtained to the case of second order nonlinear ordinary differential equations as well as to a particular case of second order nonlinear delay differential equations...

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