Almenar, Pedro; Jódar Sánchez, Lucas Antonio(MDPI AG, 2021-11)
[EN] This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n-th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Elsevier, 2012-01)
This paper presents an upper bound for the distance between a zero and a critical point of a solution of the second order linear differential equation (p(x)y¿)¿+q(x)y(x)=0(p(x)y¿)¿+q(x)y(x)=0, with p(x),q(x)>0p(x),q(x)>0. ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Elsevier, 2011-07)
This paper presents integral criteria to determine the asymptotic behaviour of the solutions of second order nonlinear differential equations of the type y¿(x)+q(x)f(y(x))=0, with q(x)>0 and f(y) odd and positive for y>0, ...
Almenar Belenguer, Pedro(Universitat Politècnica de València, 2009-09-02)
En esta memoria se construyen soluciones analítico-numéricas con cotas de error a priori de problemas mixtos relacionados con ecuaciones en derivadas parciales con coeficientes separables y condiciones de contorno de tipo ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Hindawi Publishing Corporation, 2013)
This paper presents a method to determine whether the second-order linear differential equation y(n) + q(x)y = 0 is either disfocal or nondisfocal in a fixed interval. The method is based on the recursive application of a ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(John Wiley & Sons, 2021-04)
[EN] This paper describes a recursive procedure to estimate the smallest eigenvalue of an nth-order boundary value problem under a wide set of boundary conditions. The procedure yields lower and upper bounds for that ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Hindawi Publishing Corporation, 2016)
[EN] This paper presents a modification of a recursive method described in a previous paper of the authors, which yields necessary and
sufficient conditions for the existence of solutions of a class of 𝑛�th-order linear ...
Almenar-Belenguer, Pedro; Jódar Sánchez, Lucas Antonio(Springer (Biomed Central Ltd.), 2022-07-26)
[EN] This paper provides conditions for determining the sign of all the partial derivatives of
the Green functions of n-th order boundary value problems subject to a wide set of
homogeneous two-point boundary conditions, ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Vilnius Gediminas Technical University, 2017)
[EN] This paper presents a recursive method which yields necessary and sufficient conditions for the existence of solutions of a class of n-th order linear focal boundary value problems in the interior of a given interval, ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Hindawi Publishing Corporation, 2015)
This paper presents a method that provides necessary and sufficient conditions for the existence of solutions of nth order linear boundary value problems. The method is based on the recursive application of a linear integral ...
Almenar; Pedro; Jódar Sánchez, Lucas Antonio(Hindawi Publishing Corporation, 2013)
This paper reuses an idea first devised by Kwong to obtain upper bounds for the distance between a zero and an adjacent critical point
of a solution of the second order half-linear differential equation. It also compares ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(Springer (Biomed Central Ltd.), 2021-10-14)
[EN] The purpose of this paper is to present a procedure for the estimation of the smallest eigenvalues and their associated eigenfunctions of nth order linear boundary value problems with homogeneous boundary conditions ...
Almenar, Pedro; Jódar Sánchez, Lucas Antonio(MDPI AG, 2020-05)
[EN] This paper provides results on the sign of the Green function (and its partial derivatives) of ann-th order boundary value problem subject to a wide set of homogeneous two-point boundary conditions. The dependence of ...