On the Volterra property of a boundary problem with integral gluing condition for mixed parabolic-hyperbolic equation

In the present work we consider a boundary value problem with gluing conditions of integral form for parabolic-hyperbolic type equation. We prove that the considered problem has the Volterra property. The main tools used in the work are related to the method of the integral equations and functional analysis.Comment: 18 page

Fully nonlinear fourth-order equations with functional boundary conditions

AbstractThe aim of this paper consists in to give sufficient conditions to ensure the existence and location of the solutions of a nonlinear fully fourth-order equation with functional boundary conditions. The arguments make use of the upper and lower solutions method, a ϕ-Laplacian operator and a fixed point theorem. An application of the beam theory to a nonlinear continuous model of the human spine allows to estimate its deformation under some loading forces

Periodic solutions for some phi-Laplacian and reflection equations

This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular initial and boundary value problems with reflection, which allows us to prove existence of solutions of the latter using the existence of the formerThe work was partially supported by FEDER and Ministerio de Economía y Competitividad, Spain, project MTM2013-43014-P. The second author was supported by FPU scholarship, Ministerio de Educación, Cultura y Deporte, Spain and Xunta de Galicia (Spain), project EM2014/032S

Extremal solutions for third-order nonlinear problems with upper and lower solutions in reversed order

This paper deals with the existence of extremal solutions for the third-order nonlinear boundary value problem ....info:eu-repo/semantics/publishedVersio

On Homoclinic Solutions of a Semilinear -Laplacian Difference Equation with Periodic Coefficients

We study the existence of homoclinic solutions for semilinear -Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis-Nirenberg's Mountain Pass Theorem. Several examples and remarks are givenA. Cabada partially supported by Ministerio de Educacion y Ciencia, Spain, project MTM2007-61724S

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

The System of Kaup Equations with a Self-Consistent Source in the Class of Periodic Functions

In the paper, a method of the inverse spectral problem is used to integrate the system of Kaup equations with a self-consistent source in the class of periodic functions.Метод обратной спектральной задачи применяется к интегрированию системы уравнений Каупа с самосогласованным источником в классе периодических функци