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

100%
Tsamatos P.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 3
231-242
EN
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.
2
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Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

63%
Karakostas G., Tsamatos P.
Annales Polonici Mathematici
|
2002
|
tom 78
|
nr 3
267-276
EN
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.
3
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Multiple positive solutions for a second order delay boundary value problem on the half-line

51%
Mavridis K., Philos C., Tsamatos P.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 2
173-191
EN
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 is also presented. The applicability of the main result is demonstrated by an example.
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