Displaying similar documents to “An existence theorem of positive solutions to a singular nonlinear boundary value problem”

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 ] . We assume that 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 ) . ...

Singular nonlinear problem for ordinary differential equation of the second order

Irena Rachůnková, Jan Tomeček (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the singular nonlinear problem u ' ' ( t ) + f ( t , u ( t ) , u ' ( t ) ) = 0 , u ( 0 ) = 0 , u ' ( T ) = ψ ( u ( T ) ) , where f 𝐶𝑎𝑟 ( ( 0 , T ) × D ) , D = ( 0 , ) × . We prove the existence of a solution to this problem which is positive on ( 0 , T ] under the assumption that the function f ( t , x , y ) is nonnegative and can have time singularities at t = 0 , t = T and space singularity at x = 0 . The proof is based on the Schauder fixed point theorem and on the method of a priori estimates.

Periodic boundary value problem of a fourth order differential inclusion

Marko Švec (1997)

Archivum Mathematicum

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The paper deals with the periodic boundary value problem (1) L 4 x ( t ) + a ( t ) x ( t ) F ( t , x ( t ) ) , t J = [ a , b ] , (2) L i x ( a ) = L i x ( b ) , i = 0 , 1 , 2 , 3 , where L 0 x ( t ) = a 0 x ( t ) , L i x ( t ) = a i ( t ) L i - 1 x ( t ) , i = 1 , 2 , 3 , 4 , a 0 ( t ) = a 4 ( t ) = 1 , a i ( t ) , i = 1 , 2 , 3 and a ( t ) are continuous on J , a ( t ) 0 , a i ( t ) > 0 , i = 1 , 2 , a 1 ( t ) = a 3 ( t ) · F ( t , x ) : J × R {nonempty convex compact subsets of R }, R = ( - , ) . The existence of such periodic solution is proven via Ky Fan’s fixed point theorem.

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 n × n , we call a pair of continuous functions U , V Y -compatible, if they map the space 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...