Construction of regular solutions of Schrödinger and Faddeev equations in the linear three-particle configuration limit

We study the six-dimensional Schrödinger and Faddeev equations for a three-particle system with central pairwise interactions more general than the Coulomb interactions. The regular general and particular physical solutions of such equations are represented by infinite series in integer powers of the distance from one of the particles to the center of mass of the other two particles and in some functions of the other three-particle coordinates. Constructing such functions in the angular bases formed by spherical and bispherical harmonics or by symmetrized Wigner D-functions reduces to solving simple algebraic recurrence relations. For the projections of physical solutions on the angular basis functions, we introduce the boundary conditions in the linear three-particle configuration limit.     

Spurious solutions of three-dimensional Faddeev equations

We obtain explicit spurious solutions of three-dimensional Faddeev equations written in the total angular momentum and total space parity representation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 227–242, August, 2006.     

Global regular solutions for Landau-Lifshitz equation

In this note, we prove that there exists a unique global regular solution for multidimensional Landau-Lifshitz equation if the gradient of solutions can be bounded in space L ²(0, T; L ^∞). Moreover, for the two-dimensional radial symmetric Landau-Lifshitz equation with Neumann boundary condition in the exterior domain, this hypothesis in space L ²(0, T; L ^∞) can be cancelled.     

Families of regular solutions of singular systems

The seminal 1969 paper of W.A. Harris Jr., Y. Sibuya, and L. Weinberg provided new proofs for the Perron-Lettenmeyer theorem, as well as several other classical results, and has stimulated renewed consideration of families of regular solutions of certain singular problems. In this paper we give some further applications of the method developed there and, in addition, examine some connections between the Lettenmeyer theorem and an alternative theorem which addresses a problem posed by H.L. Turrittin that dates back to an 1845 example of Briot and Bouquet     

Periodic solutions of delay impulsive differential equations

We study the following semilinear impulsive differential equation with delay:

     

On acyclicity of the set of solutions to the Cauchy problem for differential equations

The acyclicity of sets of solutions to the Cauchy problem is considered from the viewpoint of the axiomatic theory of solutions spaces of ordinary differential equations. We prove that the class of acyclic solution spaces is closed with respect to passing to the limit space. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 836–842, December, 1997 Translated by M. A. Shishkova     

Three solutions of p-Laplacian equations via a critical point theorem of Ricceri

In this paper,we consider the following quasilinear diferential equation(p(u′))′+λf(t,u)=0subject to one of the two boundary conditions:u(0)=u′(1)=0,u′(0)=u(1)=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result.     

Approximating solutions of nonlinear hybrid differential equations

We prove the existence as well as approximations of the solutions of initial value problems of first order ordinary nonlinear hybrid differential equations. We rely our results on a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. A realization is also indicated to illustrate the abstract theory developed in the paper.     

Series solutions of coupled differential equations with one regular singular point

We consider two linear second-order ordinary differential equations. r=0 is a regular singular point of these equations. Applying the classical Method of Frobenius, we do not obtain any indicial equation and therefore no solution, because the differential equations are coupled.

In this paper, we present an extended Method of Frobenius on a coupled system of two ordinary differential equations. These equations come from the micropolar theory, which is one of the three kinds of the new 3M physics.     

The existence of positive solutions of the nonlinear neutral differential equations in a Banach space

1.IntroductionTheexistenceanduniquenessofsolutionsofdelaydifferentialequationsinaBanachspacehavebeenstudiedbymanyauthors(see[1--4]).Inthispaper,weshallapplythefixedpoillttheoremstoinvestigatetheexistenceofpositivesolutionsofnonlinearneutraldifferentialdifferenceequationsinaBanachspace.LetRbethefieldofrealnumbers,andletR ={tERIt20},to>0,J=[to, co)'ConsiderthenonlinearneutraldifferentialdifferenceequationinaBanachspaceE.mI(x(t)~Zci(t)x(t~ri))' ZPj(t)fj(x(t~D))=0,(1)i=1j=1wherefiEC[P,PI,f…     

Positive solutions of singular Caputo fractional differential equations with integral boundary conditions

In this paper, we investigate the existence of positive solutions of singular super-linear (or sub-linear) integral boundary value problems for fractional differential equation involving Caputo fractional derivative. Necessary and sufficient conditions for the existence of C³[0, 1] positive solutions are given by means of the fixed point theorems on cones. Our nonlinearity f(t, x) may be singular at t = 0 and/or t = 1.     

Positive solutions of fractional differential equations with the Riesz space derivative

A new class of fractional differential equations with the Riesz–Caputo derivative is proposed and the physical meaning is introduced in this paper. The boundary value problem is investigated under some conditions. Leray–Schauder and Krasnoselskii’s fixed point theorems in a cone are adopted. Existence of positive solutions is provided. Finally, two examples with numerical solutions are given to support theoretical results.     

Existence of positive solutions to a coupled system of fractional differential equations

We consider the following system of fractional differential equations where is the Riemann‐Liouville fractional derivative of order α,f,g : [0,1] × [0, ∞ ) × [0, ∞ ) → [0, ∞ ). Sufficient conditions are provided for the existence of positive solutions to the considered problem. Copyright © 2014 John Wiley & Sons, Ltd.     

On the existence of positive solutions of second order differential equations

Using the fixed point method we prove an existence result for positive solutions of nonlinear second order ordinary differential equations. An application to semilinear Schrödinger equations in exterior domains is also presented. Mathematics Subject Classification (2000) 34C10     

Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques.     

Bifurcations of periodic solutions of delay differential equations

In this paper we develop Kaplan-Yorke's method and consider the existence of periodic solutions for some delay differential equations. We especially study Hopf and saddle-node bifurcations of periodic solutions with certain periods for these equations with parameters, and give conditions under which the bifurcations occur. We also give application examples and find that Hopf and saddle-node bifurcations often occur infinitely many times.     

Nontrivial solutions of boundary value problems of second-order difference equations

We employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second-order difference equations.     

Existence of positive solutions for higher-order functional differential equations

Under suitable conditions on f(t,y(t+θ)), the boundary value problem of higher-order functional differential equation (FDE) of the form