MULTIPLE POSITIVE PERIODIC SOLUTIONS TO SINGULAR DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY

By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.     

一类半无穷区间上奇异Sturm-LiouVille边值问题正解的存在性

利用非线性备择性定理,研究了无穷区间上一类二阶奇异Sturm-Liouville边值问题,其中f(t,u,v)可在t=0,V=0处奇异,得到了其C_p~1(0,∞)正解存在的一个判定方法。     

NOTE ON MULTIPLE POSITIVE SOLUTIONS TO NON-HOMOGENOUS MULTI-POINT BVPS FOR SECOND ORDER p-LAPLACIAN EQUATIONS

In this paper, some new sufficient conditions guaranteeing the existence of at least three positive solutions to non-homogenous multi-point boundary value problem for second order p-Laplacian equations are established. An example is presented to illustrate the main result.     

POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY

In this work,we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line.Two problems from epidemiology and combustion theory set on...     

PERIODIC SOLUTIONS TO A KIND OF p-LAPLACIAN EQUATION WITH A VARIABLE COEFFICIENT AHEAD OF THE NONLINEAR TERM

In this paper, we study the existence of periodic solutions to a kind of p-Laplacian equation, whose coefficient ahead of the nonlinear term is variable. Such a p-Laplacian equation is different from a class of previous ones. We obtain some new results by a critical point theory.     

ON SOLUTIONS TO SINGULAR FRACTIONAL DIFFERENTIAL SYSTEMS WITH CONSTANT COEFFICIENTS

In this paper, we consider solutions to singular fractional differential systems with constant coefficients involving Riemann-Liouville differential operator. At first, we study the solvability of the systems. Then we discuss the general solution to the system.     

MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.     

MULTIPLE POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

This paper is concerned with the existence of positive solutions to singular boundary value problems of functional differential equations with p-Laplacian. Under the suitable conditions,the existence of three positive solutions is esta- blished by using an abstract fixed point theorem.     

具p-Laplacian算子型奇异边值问题多重正解

本文讨论了一类具ｐ－Ｌａｐｌａｃｉａｎ算子型奇异边值问题（φｐ（ｘ＇））＇＋ａ（ｔ）ｆ（ｘ（ｔ））＝０,ｘ（０）－βｘ（０′）＝ ０,ｘ（１）＋ δｘ′（１）＝０多重正解的存在性,其中φｐ（ｘ）＝｜ｘ｜ｐ－２ｘ,ｐ＞１ 通过使用不动点指数定理, 在适当的条件下,建立了这类边值问题存在多重正解的充分条件．这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性．     

具p-Laplacian算子型奇异边值问题多重正解

本文讨论了一类具p-Laplacian算子型奇异边值问题(φp(x))＇+a(t)f(x(t))=0,x(0)-βx＇(0)=0,x(1)+δx＇(1)=0多重正解的存在性,其中φp(x)=|x|-2x,p＞1.通过使用不动点指数定理,在适当的条件下,建立了这类边值问题存在多重正解的充分条件.这些结果能被用来研究椭圆边值问题多重径向对称解的存在性.     

MULTIPLE 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 a fixed point theorem of cone expansion-compression type due to Krasnosel'skii,we obtain various new results on the existence of two positive solutions to the problem,whose coefficient is allowed to have suitable singularities. Finally,we give an example to verify our results.     

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.     

BOUNDS ON SOLUTIONS TO SOME NONLINEAR VOLTERRA INTEGRAL INEQUALITIES WITH WEAKLY SINGULAR KERNELS

Bounds on solutions to a new class of nonlinear integral inequalities with weakly singular kernels are established by the de-singularity approach.     

一类奇异无穷边值问题正解的存在性

通过构造一个特殊的锥,利用不动点指数定理,研究了无穷区间上一类二阶奇异Stuem-Liouville边值问题,得到了其$C^1_p[0,\infty)$正解存在的一个判定方法.     

EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

We study the existence of solutions to the following parabolic equation{ut-△pu=λ/|x|s|u|q-2u,(x,t)∈Ω×(0,∞),u(x,0)=f(x),x∈Ω,u(x,t)=0,(x,t)∈Ω×(0,∞),(P)}where-△pu ≡-div(|▽u|p-2▽u),1相似文献   

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER NEUMANN BOUNDARY VALUE PROBLEMS

Using the fixed point index in cones, we study the existence of one and two positive solutions to singular second order Neumann boundary value problems under some conditions, which concerns the first eigenvalue of the relevant linear problem. Our results improve and extend some known ones in the previous literature.     

带p-Laplacian算子三点奇异边值问题多个对称正解的存在性

利用凸锥上的不动点定理,研究了一类带p-Laplacian算子的微分方程三点奇异边值问题对称正解的多重性,得到了这类边值问题存在多个对称正解的充分条件.     

p-Laplacian奇异半正单调问题的非负解

运用分析的方法，建立了具有p-Laplacian算子的二阶奇异半正单调边值问题的非负解的存在性条件．     

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

11皿roduction and Main ResultsBoundary vlue probl。s(abbr．as BVP)associated with smgtllar second order ditherelltiale叩atiolls h出柏a IOllg hEtofy nd m聊dlfferem methods nd techniques h出用been sed皿ddev咖pod m OTder to obtmn——Oils qualltatn旧properties of the solutions．nr detmls,see/forInstance,papers [l－6] and the references therein．Ho。。r,only few。rks on singul。boundmpMu。Problems for suPe山near ODEs【of}6]．As》as。thorh。s,the worh on the。stenceof mlmltiple posit讨esoluti…     

一类奇异半线性反应扩散方程初值问题解的存在性

本文获得了如下的奇异半线性反应扩散方程初值问题{(e)u/(e)t-(1/tσ)△u=up+f(x),t＞0,x∈Rnlim t→0+ u (t,x)=0, x∈Rn广义解(mild solution)在L∞ loe[(0,∞);L∞(Rn)]中的存在性.其中σ＞0,0＜p＜1,f(x)非负且f(x)∈L∞(Rn).