The general method for solving the partial differential equation of any order with unknown function depending on any number of arguments and the system of such equations
K. Orlov (1978)
Matematički Vesnik
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K. Orlov (1978)
Matematički Vesnik
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K. Orlov (1978)
Matematički Vesnik
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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].
M. Greguš (1974)
Annales Polonici Mathematici
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Józef Wenety Myjak (1973)
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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A. Lasota (1975)
Annales Polonici Mathematici
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Nikolskij, S.
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Ashordia, M. (1995)
Memoirs on Differential Equations and Mathematical Physics
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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.