Second-order boundary value problems with integral boundary conditions

In this paper we investigate the existence of positive solutions of nonlocal second-order boundary value problems with integral boundary conditions.     

Positive solutions for 2p-order and 2q-order systems of singular boundary value problems with integral boundary conditions

In this paper, we study the existence, multiplicity and nonexistence of positive solutions for 2p-order and 2q-order systems of singular boundary value problems with integral boundary conditions. The results are based upon the fixed-point theorem of cone expansion and compression type due to Krasnosel’skill. Moreover, it generalizes and includes some known results.     

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

A transfer integral technique for solving a class of linear integral equations: Convergence and applications to DNA

An eigenvalue problem, the convergence difficulties that arise and a mathematical solution are considered. The eigenvalue problem is motivated by simplified models for the dissociation equilibrium between double-stranded and single-stranded DNA chains induced by temperature (thermal denaturation), and by the application of the so-called transfer integral technique. Namely, we extend the Peyrard–Bishop model for DNA melting from the original one-dimensional model to a three-dimensional one, which gives rise to an eigenvalue problem defined by a linear integral equation whose kernel is not in L²$L^2$. For the one-dimensional model, the corresponding kernel is not in L²$L^2$ either, which is related to certain convergence difficulties noticed by previous researchers. Inspired by methods from quantum scattering theory, we transform the three-dimensional eigenvalue problem, obtaining a new L²$L^2$ kernel which has improved convergence properties.     

Second order singular boundary value problems with integral boundary conditions

We study the second order singular boundary value problem

     

Eigenvalues of semi-positone Hammerstein integral equations and applications to boundary value problems

Eigenvalue intervals and the existence of finitely many positive eigenfunctions for semi-positone Hammerstein integral equations are obtained. The positive characteristic values and their upper and lower bounds of the corresponding linear Hammerstein integral operators are studied. Applications of the results are given to third-order differential equations with three-point boundary conditions.     

On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals

The behaviour of a solution to a Fredholm integral equation of the second kind on a union of open intervals is examined. The kernel of the corresponding integral operator may have diagonal singularities, information about them is given through certain estimates. The weighted spaces of smooth functions with boundary singularities containing the solution of the integral equation are described.     

Necessary and sufficient conditions for the existence of positive solutions of fourth order multi-point boundary value problems

This paper investigates the existence of positive solutions of singular multi-point boundary value problems of fourth order ordinary differential equation with p-Laplacian. A necessary and sufficient condition for the existence of C²[0,1] positive solution as well as pseudo-C³[0,1] positive solution is given by means of the fixed point theorems on cones.     

The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval

     

Positive solutions for semi-positone three-point boundary value problems

Using a fixed point theorem of generalized cone expansion and compression we present in this paper criteria which guarantee the existence of at least two positive solutions for semi-positone three-point boundary value problems with parameter λ>0$\lambda >0$ belonging to a certain interval.     

Positive solutions for second-order four-point boundary value problems with alternating coefficient

In this paper, we investigate the existence of positive solutions for a class of nonlinear second-order four-point boundary value problems with alternating coefficient. Our approach relies on the Krasnosel’skii fixed point theorem. The result of this paper is new and extent the previously known result.     

On the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearities

In this paper, we study the existence of positive solutions for the semilinear elliptic problem

     

On the stability of solutions of linear boundary value problems for a system of ordinary differential equations

Linear boundary value problems for a system of ordinary differential equations are considered. The stability of the solution with respect to small perturbations of coefficients and boundary values is investigated.