Existence of positive solutions for a fourth-order differential system

Ravi P. Agarwal; B. Kovacs; D. O'Regan

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Displaying similar documents to “Existence of positive solutions for a fourth-order differential system”

A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity

Qingliu Yao (2013)

Annales Polonici Mathematici

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We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.

Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

G. L. Karakostas, P. Ch. Tsamatos (2002)

Annales Polonici Mathematici

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We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.

The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE.

Kwong, Man Kam (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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The facial structure of the finite dimensional latticial cone.

Németh, A.B. (2004)

Mathematica Pannonica

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Diagonals of convex sets

Miroslav Fiedler, Vlastimil Pták (1978)

Czechoslovak Mathematical Journal

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The barrier cone of a convex set and the closure of the cover.

Bair, J., Dupin, J.C. (1999)

Journal of Convex Analysis

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On Krasnoselskii's cone fixed point theorem.

Kwong, Man Kam (2008)

Fixed Point Theory and Applications [electronic only]

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Positive solutions for sublinear elliptic equations

Bogdan Przeradzki, Robert Stańczy (2002)

Colloquium Mathematicae

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The existence of a positive radial solution for a sublinear elliptic boundary value problem in an exterior domain is proved, by the use of a cone compression fixed point theorem. The existence of a nonradial, positive solution for the corresponding nonradial problem is obtained by the sub- and supersolution method, under an additional monotonicity assumption.

$H$ -cones and potential theory

Nicu Boboc, Gheorghe Bucur, A. Cornea (1975)

Annales de l'institut Fourier

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The $H$ -cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an $H$ -cone. There are given an integral representation theorem and a representation theorem as an $H$ -cone of functions for which fine topology, thinnes, negligible sets and the...

Characterizations of balayages.

Eriksson-Bique, Sirkka-Liisa (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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Local and global $σ$ -cone porosity

Petr Holický (1993)

Acta Universitatis Carolinae. Mathematica et Physica

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Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

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.