201 research outputs found
Characterization of the Solvability of Generalized Constrained Variational Equations
In a general context, that of the locally convex spaces, we characterize the existence of a solution for certain variational equations with constraints. For the normed case and in the presence of some kind of compactness of the closed unit ball, more specifically, when we deal with reflexive spaces or, in a more general way, with dual spaces, we deduce results implying the existence of a unique weak solution for a wide class of linear elliptic boundary value problems that do not admit a classical treatment. Finally, we apply our statements to the study of linear impulsive differential equations, extending previously stated results.This research is partially supported by the Junta de Andaluca Grant FQM359
Variational Approach to Impulsive Problems: A Survey of Recent Results
We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions
Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions
Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results
Semi-linear impulsive higher order boundary value problems
This paper considers two-point higher order impulsive boundary value problems, with a strongly nonlinear fully differential equation with an increasing homeomorphism. It is stressed that the impulsive effects are defined by very general functions,
that can depend on the unknown function and its derivatives, till order n − 1.
The arguments are based on the lower and upper solutions method, together with
Leray–Schauder fixed point theorem. An application, to estimate the bending of a onesided clamped beam under some impulsive forces, is given in the last section
Lagrangian Variational Framework for Boundary Value Problems
A boundary value problem is commonly associated with constraints imposed on a
system at its boundary. We advance here an alternative point of view treating
the system as interacting "boundary" and "interior" subsystems. This view is
implemented through a Lagrangian framework that allows to account for (i) a
variety of forces including dissipative acting at the boundary; (ii) a
multitude of features of interactions between the boundary and the interior
fields when the boundary fields may differ from the boundary limit of the
interior fields; (iii) detailed pictures of the energy distribution and its
flow; (iv) linear and nonlinear effects. We provide a number of elucidating
examples of the structured boundary and its interactions with the system
interior. We also show that the proposed approach covers the well known
boundary value problems.Comment: 41 pages, 3 figure
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