In this paper we give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem Du + a(t)f(u) = 0, 0 < t < 1,1 < � � 2,

/pdf/positive-solutions-of-a-boundary-value-problem-for-a-4aivevv6iz.pdf

Positive solutions of a boundary value problem for a nonlinear fractional differential equation.

. In this paper we prove that the collection of all weakly distributive lattice ordered groups is a radical class and that it fails to be a torsion class.

Lattice ordered groups

Oscillation Theory for Functional Differential Equations (L. H. Erbe, Q. K. Kong, and B. G. Zhang)

Latterly, many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, to a series of time-fractional partial differential equations. Unlike the normal case derivative, the differential order in such equations is with a fractional order, which will lead to new challenges for numerical simulation. The purpose of this analysis is to introduce the reproducing kernel Hilbert space method for treating classes of time-fractional partial differential equations subject to Neumann boundary conditions with parameters derivative arising in fluid-mechanics, chemical reactions, elasticity, anomalous diffusion, and population growth models. The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. Numerical experiments with different order derivatives degree are performed to support the theoretical analyses which are acquired by interrupting the n-term of the exact solutions. Finally, the obtained outcomes showed that the proposed method is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional Neumann problems.

Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions

The aim of the present analysis is to implement a relatively recent computational algorithm, reproducing kernel Hilbert space, for obtaining the solutions of systems of first-order, two-point boundary value problems for ordinary differential equations. The reproducing kernel Hilbert space is constructed in which the initial–final conditions of the systems are satisfied. Whilst, three smooth kernel functions are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods.

Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm

The authors consider the higher order boundary-value problem u (n) (t) = q(t)f(u(t)), 0 t 1, where n 4 is an integer, and p 2 (1/2,1) is a constant. Sucient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

/pdf/positive-solutions-of-a-nonlinear-higher-order-boundary-4veqgmw1ro.pdf

Positive solutions of a nonlinear higher order boundary-value problem

The authors study a higher order three point boundary value problem. Estimates for positive solutions are given; these estimates improve some recent results in the literature. Using these estimates, new sufficient conditions for the existence and nonexistence of positive solutions of the problem are obtained. An example illustrating the results is included.

pdf/positive-solutions-of-a-nonlinear-higher-order-boundary-ilc9726e4z.pdf

In this paper, the authors consider the boundary value problem (E) x (2m) (t) + (-1) m+1 f(x(t)) = 0, 0 < t < 1, (B) x (2i) (0) = x (2i) (1) = 0, i = 0, 1, 2, …, m - 1, and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.

/pdf/multiple-symmetric-positive-solutions-of-a-class-of-boundary-37e7yqqp5e.pdf

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

The authors consider booundary value problems for fourth order ordinary differential equations of the form with the boundary conditions or They give sufficient conditions for the problems (E)-(B1) and (E)-(B2) to have at least one positive solutions. They also give sufficient conditions for these problems to have no positive solutions. Examples to illustrate that the results are sharp are also included.

Existnence and nonexistence of positive solutions of fourth order nonlinear boundary value problems

BO YANGAbstract. We consider a boundary-value problem for the beam equation, inwhich the boundary conditions mean that the beam is embedded at one endand fastened with a sliding clamp at the other end. Some priori estimatesto the positive solutions for the boundary-value problem are obtained. Suﬃ-cient conditions for the existence and nonexistence of positive solutions for theboundary-value problem are established.

/pdf/positive-solutions-for-the-beam-equation-under-certain-3orllxxq12.pdf

Positive solutions for the beam equation under certain boundary conditions

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Papers

Positive solutions of a nonlinear higher order boundary-value problem

Positive solutions of a nonlinear higher order boundary-value problem

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

Existnence and nonexistence of positive solutions of fourth order nonlinear boundary value problems

Positive solutions for the beam equation under certain boundary conditions