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Jolanta Przybycin (1997)
Annales Polonici Mathematici
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We establish the existence and uniqueness theorems for a linear and a nonlinear fourth-order boundary value problem. The results obtained generalize the results of Usmani [4] and Yang [5]. The methods used are based, in principle, on [3], [5].
Ilja Martišovitš (1999)
Mathematica Slovaca
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M. Greguš (1974)
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].
Józef Wenety Myjak (1973)
Annales Polonici Mathematici
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Gupta, Chaitan P. (1995)
International Journal of Mathematics and Mathematical Sciences
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Henderson, Johnny (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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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.
A. Lasota (1975)
Annales Polonici Mathematici
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Boris Rudolf (2000)
Archivum Mathematicum
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In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.