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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.

Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral

Salvador Sánchez-Perales, Francisco J. Mendoza-Torres (2020)

Czechoslovak Mathematical Journal

In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation - y ' ' + q y = f , where q and f are Henstock-Kurzweil integrable functions on [ a , b ] . Results presented in this article are generalizations of the classical results for the Lebesgue integral.

Boundary value problems with compatible boundary conditions

George L. Karakostas, P. K. Palamides (2005)

Czechoslovak Mathematical Journal

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

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