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Boundary value problems for first order multivalued differential systems

Abdelkader Boucherif, N.Chiboub-Fellah Merabet (2005)

Archivum Mathematicum

We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.

Boundary value problems for higher order ordinary differential equations

Armando Majorana, Salvatore A. Marano (1994)

Commentationes Mathematicae Universitatis Carolinae

Let f : [ a , b ] × ℝ n + 1 → ℝ be a Carath’eodory’s function. Let { t h } , with t h ∈ [ a , b ] , and { x h } be two real sequences. In this paper, the family of boundary value problems x ( k ) = f t , x , x ' , ... , x ( n ) x ( i ) ( t i ) = x i , i = 0 , 1 , ... , k - 1 ( k = n + 1 , n + 2 , n + 3 , ... ) is considered. It is proved that these boundary value problems admit at least a solution for each k ≥ ν , where ν ≥ n + 1 is a suitable integer. Some particular cases, obtained by specializing the sequence { t h } , are pointed out. Similar results are also proved for the Picard problem.

Boundary value problems for nonlinear perturbations of some ϕ-Laplacians

J. Mawhin (2007)

Banach Center Publications

This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder...

Boundary value problems for ODEs

Tadeusz Jankowski (2003)

Czechoslovak Mathematical Journal

We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

Boundary value problems for systems of functional differential equations

Tadeusz Jankowski (2002)

Applications of Mathematics

Algorithms for finding an approximate solution of boundary value problems for systems of functional ordinary differential equations are studied. Sufficient conditions for consistency and convergence of these methods are given. In the last section, a construction of methods of arbitrary order is presented.

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