Existence of Nonnegative Solutions to Singular Semi-positone Problems

In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.     

Existence of Positive Solutions to Fourth Order Quasilinear Boundary Value Problems

In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some fourth-order beam equation boundary value problems is obtained. The emphasis is put on that the nonlinear term is dependent on all lower order derivatives.     

Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings

Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.     

Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems

The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation （Ф（x＇））＇＋μQ（t, x, x＇） = 0 satisfying the Dirichlet boundary conditions x（0） = x（T） = 0. Here Q is a continuous function on the set [0, T] × （0, ∞） ~ （R ／ {0}） of the semipositone type and Q is singular at the value zero of its phase variables.     

Existence of Solutions for Singular Boundary Value Problems

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The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates.     

New Solutions for Some Planar N-body Problems

W七study the motion of planar N body problems with mass。‘(乞=1,2,…,N),whieh 15govered饰NQ自m、认+aV(g) aq;0,(1)where、、任RZ 15 the position of the乞一th body,andV(g)15 the Newtonian potentialV(、)一V(、;,一。、)一U(。)一艺 m‘钩}q‘一引(2) 1三乞(j三NW七want to look for the non-eireular and non一elliPtieall一Periodiesolution.LetH‘一W‘,’(誓,*2)={u,它任石2(R,RZ),。(t+1)=u(t)},(3)eosssin口(4)J/‘飞、 一一 ‘、.,了口 月︸ r了‘、几 O‘、、.夕/,,工n︶01上/了.龟、 一一 AFor Planar 4n…     

Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations

This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt ＋ α1 uδ^2u/δx^2 ＋ βδ^3u/δx^3 ＋ γδ^5u/δx^5 = 0, （x,t）∈ E R^2, and δu/δt ＋ α2 δu/δx δ^2u/δx^2 ＋ βδ^3u/δx^3 ＋ γδ^5u/δx^5 = 0, （x, t） ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0（x） ∈ H^s（R）, and s ≥ 5/4 for the first equation and s≥301/108 for the second equation.     

Existence of Positive Solutions to a Fractional-Kirchhoff System

Let Ω be a bounded smooth domain in R^N(N≥3).Assuming that 0 0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,■Under some assumptions of h_i(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1) by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establis...     

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

Ｇｌｏｂａｌ　Ｅｘｉｓｔｅｎｃｅ　ａｎｄ　Ｌｉｆｅｓｐａｎ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｔｏ　ｔｈｅ　Ｃａｕｃｈｙ　Ｐｒｏｂｌｅｍｓ　ｆｏｒ　ｔｈｅ　Ｎｏｎｌｉｎｅａｒ　Ｓｃｈｒｏｄｉｎｇｅｒ　ＥｑｕａｔｉｏｎｓＧｌｏｂａｌＥｘｉｓｔｅｎｃｅａｎｄＬｉ...     

Existence of Solutions to a Singular Initial Value Problem

Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.     

Existence of Solutions for Nonlinear Implicit Complementarity Problems in Reflexive Banach Spaces

51.IntroductionNonlinearcomp1ementaritytheoryhasemergedasaninterestingandfascinatingbranchofapplicablemathematics.Thistheoryhasbecomearichsourceofinspirationandmotivationforscientistsandengineerstoalargenumberofproblemsarisingincontactproblemsinelasticity,fluidflowthroughporousmedia,generalequilibriumoftransportationandeconomics,optimiza-tionandcontrolproblems,etc.IthasbeenshownbyKaramardian[8jthatiftheconvexsetin-volvedinavariationalinequalityproblemandacomplmentarityproblemisaconvexcone,then…     

Existence of Positive Solutions for Second-Order m-Point Boundary Value Problems on Time Scales

This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.     

Existence and Uniqueness of Solutions to Boundary Value Problems for Ordinary Differential Equations Across Many Resonant Points

Ｅｘｉｓｔｅｎｃｅ　ａｎｄ　Ｕｎｉｑｕｅｎｅｓｓ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｔｏ　Ｂｏｕｎｄａｒｙ　Ｖａｌｕｅ　Ｐｒｏｂｌｅｍｓ　ｆｏｒ　Ｏｒｄｉｎａｒｙ　Ｄｉｆｆｅｒｅｎｔｉａｌ　Ｅｑｕａｔｉｏｎｓ　Ａｃｒｏｓｓ　Ｍａｎｙ　Ｒｅｓｏｎａｎｔ　Ｐｏｉ...     

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures.     

Existence and Uniqueness of Solutions to Random Impulsive Differential Systems

The existence and uniqueness in mean square of solutions to certain random impulsive differentialsystems is discussed in this paper.Cauchy-Schwarz inequality,Lipschtiz condition and techniques in stochasticanalysis are employed in achieve the desired results.     

Existence and Uniqueness of Solutions of Some Cauchy Problems for the Emden–Fowler Equation

Differential Equations - We consider the Cauchy problem for the Emden–Fowler equation $$y^{prime {}prime }-x^ay^{sigma }=0 $$ with parameters $$ain mathbb {R} $$ and $$sigma <0...     

Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions

In this paper, an existence theorem for solutions to the generalized Ky Fan Inequality problem is obtained by means of the Kakutani-Fan-Glicksberg fixed-point theorem without imposing the condition that the dual of the ordering cone has a weak* compact base. In addition, the stability of the solution set is shown.     

Convergence in Distribution of Optimal Solutions to Stochastic Optimization Problems

1.IntroductionDistributionproblemsareofgreatimportanceinstochasticoptimizationandstatis-tics.Usuallythiskindofproblemscanbedescribedinthefollowingform:wheref(x,w)isafuncti0ndefinedonR"xflandSisasubsetin'R".Because0fc0mplexityoftheproblems,ingeneral,onecangetonlytheirapproximatesolutions.Thefollowingtypeofapproximationis0ftenused:Letuscall(2)thefirsttype0fapproximation.DenotebyZ(w),A(w)theoptima1valueandoptimalsolutionsetofproblem(1)respectivelyandbyZk(w),Ak(w)thecorrespondingonesofproblem(…     

Existence of Multiple Positive Solutions for Fourth Order Two－point Boundary Value Problems

The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:{u′″(t)=a(t)f(u(t)),t∈[0,1],;a1u(0)-b1u′(0)-c1u(1) d1u′(1)=0,;a2u″(0)-b2u′″(0)=c2u″(1) d2u′″(1)=0.Several existence theorems on multiple positive solutions to the problems are obtained,ad some examples are given to show the validity of these results.