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positive solutions of Sub-Linear Semi-Positone Boundary Value Problem System

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Journal of Mathematical Research and Exposition 2008年第2期28卷 305-315页

作者： XU Xi An Department of Mathematics Xuzhou Normal University Jiangsu 221116 China

In this paper, we study the existence of positive solutions of a sub-linear semi-positone differential boundary value problems system with positive parameter. We prove that the semipositone differential boundary value... 详细信息

关键词： semi-positone differential boundary value problems system the fixed point index positive solutions

positive solutions for Nonlinear Second-Order Boundary Value Problem of Delay Differential Equation

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Journal of Mathematical Research and Exposition 2008年第3期28卷 720-726页

作者： LI Zhi-long School of Informational Management Jiangxi University of Finance and Economics Jiangxi 330013 China

In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.

关键词： second-order boundary value problem delay differential equation positive solutions fixed point index.

positive solutions to a Singular Third-Order Three-Point Boundary Value Problem

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Journal of Mathematical Research and Exposition 2011年第2期31卷 287-294页

作者： Hong Ping WU College of Mathematics and Information Science Northwest Normal University Gansu 730070 P. R. China

In this paper,we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problemu （t） = λa（t）f（t,u（t））,u（0） = u （1） = u （η） = 0,where λ is a positive parameter and 0 ≤ η 1 2 .By using the classical Krasnosel’skii’s fixed point theorem in cone,we obtain various new results on the existence of positive solution,and the solution is strictly *** we give an example.

关键词： positive solutions singular third-order three-point BVP fixed point theorem

EXISTENCE OF positive solutions TO SEMILINEAR ELLIPTIC SYSTEMS IN R^N WITH ZERO MASS

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Acta Mathematica Scientia 2013年第4期33卷 913-928页

作者：李工宝叶红雨 School of Mathematics and Statistics Central China Normal University

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.

关键词： existence positive solutions elliptic system linking geometric structure zero mass case

MULTIPLICITY OF positive solutions FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

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Acta Mathematica Scientia 2018年第2期38卷 497-518页

作者：廖家锋蒲洋唐春雷 School of Mathematics and Statistics Southwest University Chongqing 400715 China School of Mathematics and Information China West Normal University Nanchong 637002 China

In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.

关键词： Semilinear elliptic equations critical growth positive solutions Nehari method variational method

positive solutions for First-order PBVPs on Time Scales

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Chinese Quarterly Journal of Mathematics 2012年第3期27卷 337-343页

作者： SONG Chang-xiu School of Applied Mathematics Guangdong University of Technology Guangzhou 510006 China

In this paper, the author studies the following nonlinear dynamic equation {x△(t) = r(t)x(σ(t)) + f(t, x(σ(t))), t ∈ [0, T ], x(0) = x(σ(T )). By applying and improving the generalized form of Leggett-Williams fi... 详细信息

关键词： time scale positive solutions fixed point

TWO positive solutions TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

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Acta Mathematica Scientia 2011年第1期31卷 29-38页

作者：李宇华梁占平 School of Mathematical Sciences Shanxi University

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.

关键词： Three-point singular boundary value problem positive solutions fixed point index

Multiple positive solutions for a Nonlinear Elliptic Equation Involving Hardy–Sobolev–Maz'ya Term

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Acta Mathematica Sinica,English Series 2015年第6期31卷 893-912页

作者： Shuang Jie PENG Jing YANG School of Mathematics and Statistics Central China Normal University

In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz＇ya term：-Δu-λ u/｜y｜2 = （｜u｜pt-1u）/｜y｜t ＋ μf（x）, x∈ Ω,where Ω is a bounded domain in RN（N ≥ 2）, 0 ∈ Ω, x = （y, z） ∈ Rk ×RN-k and pt = （N＋2-2t）/（N-2）（0 ≤ t ≤ 2）. For f（x） ∈ C1（Ω）／positive solutions, we show that there exists a constant μ＊〉0 such that the problem possesses at least two positive solutions if μ ∈ （0, μ＊） and at least one positive solution if μ = μ＊. Furthermore, there are no positive solutions if μ ∈ （μ＊,＋∞）.

关键词： Hardy-Sobolev-Maz'ya inequality Mountain Pass Lemma positive solutions subsolutionand supersolution

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

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Applied Mathematics and Mechanics(English Edition) 2009年第11期30卷 1461-1468页

作者：刘冠琦王玉文史峻平 Y. Y. Tseng Functional Analysis Research Center and Department of Mathematics Harbin Normal University Department of Mathematics College of William and Mary

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.

关键词： semilinear equation Allee effect positive solutions existence