Symmetric Positive Solutions of Nonlinear Singular Second-order Three-point Boundary Value Problem

In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0<t<1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.

RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.

Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian

This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.

A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION

The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.

PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.

NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.

A CLASS OF SINGULARLY PERTURBED ROBIN BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATION

The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem the existence,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.

The Existence and Multiplicity of Solutions for Singular Boundary Value Systems with p-Laplacian

This paper presents sufficient conditions for the existence of positive solutions for the fourth-order boundary value problem system with p-Laplacian operator. The existence of single or multiple positive solutions for the system is showed through the fixed point index theory in cones under some assumptions.

SINGULAR PERTURBATIONS OF A HIGHER-ORDER SCALAR NONLINEAR BOUNDARY VALUE PROBLEM

In the present paper, the singular perturbations for the higher-order scalar nonlinear boundary value problem epsilon(2)y(n)=f(t,epsilon y,y',...,y((n-2)),epsilon y((n-1)), t is an element of[0,1] H1(y(0,epsilon),...,y((n-3))(0,epsilon),epsilon y((n-2))(0,epsilon),epsilon y((n-1))(0,epsilon),epsilon)=0, H2(y(0,epsilon),y((n-1))(0,epsilon),y(1,epsilon)...,y((n-1))(1,epsilon),epsilon=0 are studied, where epsilon > 0 is a small parameter, n greater than or equal to 2. Under some mild assumptions, we prove the existence and local uniqueness of the perturbed solution and give out the uniformly valid asymptotic expansions up to its nth-order derivative function by employing the Banach/Picard fixed-point theorem. Then the existing results are extended and improved.

EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

Development of a Best Answer Recommendation Model in a Community Question Answering (CQA) System

In this work, a best answer recommendation model is proposed for a Question Answering (QA) system. A Community Question Answering System was subsequently developed based on the model. The system applies Brouwer Fixed Point Theorem to prove the existence of the desired voter scoring function and Normalized Google Distance (NGD) to show closeness between words before an answer is suggested to users. Answers are ranked according to their Fixed-Point Score (FPS) for each question. Thereafter, the highest scored answer is chosen as the FPS Best Answer (BA). For each question asked by user, the system applies NGD to check if similar or related questions with the best answer had been asked and stored in the database. When similar or related questions with the best answer are not found in the database, Brouwer Fixed point is used to calculate the best answer from the pool of answers on a question then the best answer is stored in the NGD data-table for recommendation purpose. The system was implemented using PHP scripting language, MySQL for database management, JQuery, and Apache. The system was evaluated using standard metrics: Reciprocal Rank, Mean Reciprocal Rank (MRR) and Discounted Cumulative Gain (DCG). The system eliminated longer waiting time faced by askers in a community question answering system. The developed system can be used for research and learning purposes.

MULTIPLE POSITIVE SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER ODES

This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

Existence Theory for Single and Multiple Positive Solutions to Singular Boundary Value Problems for Second-order Differential Systems P-Laplacian

In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.

A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE

In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.

EXISTENCE OF POSITIVE SOLUTION TO SUPERLINEAR SEMIPOSITONE SINGULAR m-POINT BOUNDARY VALUE PROBLEMS

Sufficient conditions for the existence of positive solution to superlinear semi-positone singular m-point boundary value problem are given by cone expansion and compression theorem in norm type.

EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.

MULTIPLE POSITIVE SOLUTIONS OF A CLASS OF THREE-POINT SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence theorem for three positive solutions is presented for the singular nonlinear boundary value problem by applying the extended Five Functionals fixed point theorem.

Positive Solution for a Singular Fourth-Order Differential System

In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 < t < 1, -φ” = μg (t, u, u”), 0 < t < 1, u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0;where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.