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Existence of nonzero nonnegative solutions of semilinear equations at resonance

Michal Fečkan (1998)

Commentationes Mathematicae Universitatis Carolinae

The existence of nonzero nonnegative solutions are established for semilinear equations at resonance with the zero solution and possessing at most linear growth. Applications are given to nonlinear boundary value problems of ordinary differential equations.

Existence of one-signed solutions of nonlinear four-point boundary value problems

Ruyun Ma, Ruipeng Chen (2012)

Czechoslovak Mathematical Journal

In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems - u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) and u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) , where ε ( 0 , 1 / 2 ) , M ( 0 , ) is a constant and r > 0 is a parameter, g C ( [ 0 , 1 ] , ( 0 , + ) ) , f C ( , ) with s f ( s ) > 0 for s 0 . The proof of the main results is based upon bifurcation techniques.

Existence of positive solutions for a class of arbitrary order boundary value problems involving nonlinear functionals

Kyriakos G. Mavridis (2014)

Annales Polonici Mathematici

We give conditions which guarantee the existence of positive solutions for a variety of arbitrary order boundary value problems for which all boundary conditions involve functionals, using the well-known Krasnosel'skiĭ fixed point theorem. The conditions presented here deal with a variety of problems, which correspond to various functionals, in a uniform way. The applicability of the results obtained is demonstrated by a numerical application.

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina Boucenna, Toufik Moussaoui (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.

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