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 a singular multi-point third-order boundary value problem on the half-line

Zakia Benbaziz, Smail Djebali (2020)

Mathematica Bohemica

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We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f ( t , x , y ) which satisfies upper and lower-homogeneity conditions in the space variables x , y may be also singular at time t = 0 . Two examples...

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.