A general theory of integral transforms and its applications
A generalization of a theorem of Mammana
We prove that any linear ordinary differential operator with complex-valued coefficients continuous in an interval I can be factored into a product of first-order operators globally defined on I. This generalizes a theorem of Mammana for the case of real-valued coefficients.
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
A generalization of rotations and hyperbolic matrices and its applications.
A generalization of the Hille--Yosida theorem to the case of degenerate semigroups in locally convex spaces.
A generalization of the Landesman-Lazer condition.
A generalization of Tichonov theorem
A generalized Fuc̆ik type eigenvalue problem for p-Laplacian.
A generalized Hankel transformation
A generalized periodic boundary value problem for the one-dimensional p-Laplacian
The generalized periodic boundary value problem -[g(u’)]’ = f(t,u,u’), a < t < b, with u(a) = ξu(b) + c and u’(b) = ηu’(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, , p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.
A generalized upper and lower solutions method for nonlinear second order ordinary differential equations.
A general-weighted Sturm-Liouville problem
A geometric analysis of a singular ODE related to the study of a quasilinear PDE.
A geometric approach to integrability conditions for Riccati equations.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A global curve of stable, positive solutions for a -Laplacian problem.
A global description of the positive solutions of sublinear second-order discrete boundary value problems.
A global factorization theorem for the ZS-AKNS system.
A gradient inequality at infinity for tame functions.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A Gronwall-like inequality and its applications
A generalized Gronwall-like inequality is established and applied in obtaining a right saturated solution for a class of differential equations and in estimating the solution of an evolution equation for the so called hidden variables.