Transformations of difference equations. II.
Currie, Sonja, Love, Anne D. (2010)
Advances in Difference Equations [electronic only]
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Currie, Sonja, Love, Anne D. (2010)
Advances in Difference Equations [electronic only]
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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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Józef Wenety Myjak (1973)
Annales Polonici Mathematici
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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.
Eloe, Paul W. (2004)
Advances in Difference Equations [electronic only]
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Henderson, Johnny (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Jenkinson, Oliver (2000)
Experimental Mathematics
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Emil Vitásek (2000)
Applications of Mathematics
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It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems. ...