Asymptotic properties of solutions of a linear-conjugation boundary-value problem

A. M. Razmadze Mathematics Institute, Georgian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 3, pp. 348–357, June, 1990.     

Bifurcation of solutions of a linear Fredholm boundary-value problem

We establish constructive conditions for the appearance of solutions of a linear Fredholm boundary-value problem for a system of ordinary differential equations in the critical case and propose an iterative procedure for finding these solutions. The range of values of a small parameter for which the indicated iterative procedure is convergent is estimated. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1148–1152, August, 2007.     

Existence of three solutions to a second-order nonhomogeneous multipoint boundary-value problem

This paper is concerned with a nonhomogeneous multipoint boundary-value problem (BVP) of a second-order differential equation with one-dimensional p-Laplacian. Using multiple fixed-point theorems, new sufficient conditions to guarantee the existence of at least three solutions of this BVP are established. An example is presented to illustrate the main results. The first emphasis of this paper is to show that the approach to get three positive solutions of a BVP by using multiple fixed-point theorems can be extended to treat nonhomogeneous BVPs. The second emphasis is put on the nonlinear term f involved with the first-order delta operator.     

Multiple solutions for a two-point boundary value problem

In this paper, using a recent result of Ricceri, we prove two multiplicity theorems for the problem −u^″=λf(u)+μg(x,u), u(0)=u(1)=0, extending a previous result that G. Bonanno obtained for μ=0.     

Global solutions of a two-dimensional initial boundary-value problem for a system of semilinear magnetoelasticity equations

We prove the theorem on the existence and uniqueness of global solutions of a system of semilinear magnetoelasticity equations in a two-dimensional space.     

Nonzero solutions to a two-point boundary-value periodic problem for differential equations with maxima

We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.     

Method of accelerated convergence for the construction of solutions of a Noetherian boundary-value problem

We study the problem of finding conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. A new iterative procedure with accelerated convergence is proposed for the construction of solutions of a weakly nonlinear Noetherian boundary-value problem for a system of ordinary differential equations in the critical case. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1587–1601, December, 2008.     

Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces

This paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary-value problem of second-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. The nonexistence of a positive solution is also studied.     

Bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations

This paper studies the bifurcation of positive solutions for a three-point boundary-value problem of nonlinear fractional differential equations with parameter. Using the topological degree theory and the bifurcation technique, the existence of positive solutions is investigated and some sufficient conditions are obtained. The study of two illustrative examples shows that the obtained new results are effective.     

On a two-point boundary-value problem in geophysics

We present some results on the existence and uniqueness of solutions to a two-point boundary-value problem that models gyre flows in rotating spherical coordinates.     

Multiple solutions for a neumann problem in an exterior domain

In this paper, we study the existence of multiple solutions of nonlinear elliptic problems in an exterior domain with Neumann boundary conditions.     

On a boundary-value problem solvability condition

We prove a sufficient condition for the solvability of a two-point problem.Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 247–250, February, 1973.