Displaying similar documents to “Singular nonlinear problem for ordinary differential equation of the second order”

Strong singularities in mixed boundary value problems

Irena Rachůnková (2006)

Mathematica Bohemica

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We study singular boundary value problems with mixed boundary conditions of the form ( p ( t ) u ' ) ' + p ( t ) f ( t , u , p ( t ) u ' ) = 0 , lim t → 0 + p ( t ) u ' ( t ) = 0 , u ( T ) = 0 , where [ 0 , T ] ⊂ ℝ . We assume that ℝ 2 , f satisfies the Carathéodory conditions on ( 0 , T ) × p ∈ C [ 0 , T ] and 1 / p need not be integrable on [ 0 , T ] . Here f can have time singularities at t = 0 and/or t = T and a space singularity at x = 0 . Moreover, f can change its sign. Provided f is nonnegative it can have even a space singularity at y = 0 . We present conditions for the existence of solutions positive on [ 0 , T ) . ...

An existence theorem of positive solutions to a singular nonlinear boundary value problem

Gabriele Bonanno (1995)

Commentationes Mathematicae Universitatis Carolinae

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In this note we consider the boundary value problem y ' ' = f ( x , y , y ' ) ( x ∈ [ 0 , X ] ; X > 0 ) , y ( 0 ) = 0 , y ( X ) = a > 0 ; where f is a real function which may be singular at y = 0 . We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O’Regan [J. Differential Equations 84 (1990), 228–251].

Singular φ -Laplacian third-order BVPs with derivative dependance

Smaïl Djebali, Ouiza Saifi (2016)

Archivum Mathematicum

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This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a φ -Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition...

On the differentiability of certain saltus functions

Gerald Kuba (2011)

Colloquium Mathematicae

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We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that g ' ( x ) = 2 x for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.

Boundary value problems with compatible boundary conditions

George L. Karakostas, P. K. Palamides (2005)

Czechoslovak Mathematical Journal

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If Y is a subset of the space ℝ n × ℝ n , we call a pair of continuous functions U , V Y -compatible, if they map the space ℝ n into itself and satisfy U x · V y ≥ 0 , for all ( x , y ) ∈ Y with x · y ≥ 0 . (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n -dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its...