Displaying similar documents to “Bifurcation theory of the time-dependent von Kármán equations”

Explicit solutions for Sturm-Liouville operator problems (II).

Lucas Jódar Sánchez (1987)

Stochastica

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It is proved that the resolution problem of a Sturm-Liouville operator problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of the corresponding algebraic operator equation. Existence and uniqueness conditions for the existence of nontrivial solutions of the problem and explicit expressions of them are given.

Explicit solutions for non homogeneous Sturm-Liouville operators problems.

Lucas Jódar Sánchez (1989)

Publicacions Matemàtiques

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In this paper we study existence and sufficiency conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X'' - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given.

An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.

Lucas A. Jódar Sanchez (1988)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and...

Uniqueness of positive solutions of nonlinear second order systems.

Robert Dalmasso (1995)

Revista Matemática Iberoamericana

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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.