Displaying similar documents to “Uniformly enclosing discretization methods for semilinear boundary value problems”

Positive solutions to nonlinear singular second order boundary value problems

Gabriele Bonanno (1996)

Annales Polonici Mathematici

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Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point...

Heteroclinic orbits in plane dynamical systems

Luisa Malaguti, Cristina Marcelli (2002)

Archivum Mathematicum

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We consider general second order boundary value problems on the whole line of the type u ' ' = h ( t , u , u ' ) , u ( - ∞ ) = 0 , u ( + ∞ ) = 1 , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the ( u , u ' ) plane dynamical system.

An existence result for nonlinear evolution equations of second order

Dimitrios A. Kandilakis (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.