Remarks on a three-point boundary value problem in a differential equation of the third order
M. Greguš (1974)
Annales Polonici Mathematici
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M. Greguš (1974)
Annales Polonici Mathematici
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K. S. Padmanabhan, R. Parvatham (1976)
Annales Polonici Mathematici
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Jenkinson, Oliver (2000)
Experimental Mathematics
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P. Ch. Tsamatos (2004)
Annales Polonici Mathematici
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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.
Nikolskij, S.
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A. Lasota (1975)
Annales Polonici Mathematici
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Henderson, Johnny (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Ashordia, M. (1995)
Memoirs on Differential Equations and Mathematical Physics
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Slovan, Jakub
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A. Lasota (1980)
Annales Polonici Mathematici
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Jan Popiołek (1997)
Annales Polonici Mathematici
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We prove the existence of solutions of some boundary-value problems for partial differential equations of order higher than two. The general idea is similar to that in [1]. We make an essential use of the results of our paper [12].