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Acta Mathematica Scientia 2018年第4期38卷 1121-1142页

作者： Shinji ADACHI Masataka SHIBATA Tatsuya WATANABE Department of Mathematical and Systems Engineering Faculty of Engineering Shizuoka University 3-5-1 Johoku Naka-ku Hamarnatsu 432-8551 Japan Department of Mathematics Tokyo Institute of Technology 2-12-1 Oh-okayama Meguro-ku Tokyo 15248551 Japan Department of Mathematics Faculty of Science Kyoto Sangyo University Motoyama Kamigamo Kita-ku Kyoto 603-8555 Japan

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.

关键词： positive radial solution uniqueness non-degeneracy shooting method

EXISTENCE OF positive radial solutionS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS

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Applied Mathematics and Mechanics(English Edition) 2002年第12期23卷 1452-1457页

作者： YAO Qing-liu(姚庆六) MA Qin-sheng(马勤生) Department of Applied Mathematics Nanjing University of EconomicsNanjing 210003 P R China College of Mathematics and Information Science Northwest Normal University Lanzhou 730070 P R China

Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.

关键词： second-order elliptic equation annular domain positive radial solution

EXISTENCE OF positive radial solutionS FOR SINGULAR ELLIPTIC SYSTEMS

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Applied Mathematics(A Journal of Chinese Universities) 2001年第2期16卷 141-148页

作者： Wan Aying Jiang DaqingDept.ofMath.,HulunberCollege,Hailar021008.Dept.ofMath.,NortheastNormalUniv.,Changchun130024 Dept. of Math. Hulunber College Hailar Dept. of Math. Northeast Normal Univ. Changchun

The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0 详细信息

The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0

关键词： positive radial solution elliptic system singular existence.

Several Existence Theorems for positive radial solutions to a Semilinear Elliptic BVP

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Northeastern Mathematical Journal 2001年第2期17卷 169-174页

作者：姚庆六 Department of Mathematics Northwest Normal University Lanzhou 730070

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X| 详细信息

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.

关键词： second order elliptic equation Dirichlet BVP in annulus positive radial solution existence theorem

Uniqueness of positive radial solutions for a Class of Semipositone Systems on the Exterior of a Ball

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Applied Mathematics 2021年第3期12卷 131-146页

作者： Alhussein Mohamed Khalid Ahmed Abbakar Abuzar Awad Omer Khalil Bechir Mahamat Acyl Abdoulaye Ali Youssouf Mohammed Mousa College of Mathematics and Statistics Northwest Normal University Lanzhou China Department of Mathematics and Physics Faculty of Education University of Gadarif Gadarif Sudan Department of Science College of Education Sudan University of Science and Technology Khartoum Sudan

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.

关键词： Elliptic System positive radial solution Exterior Domains Fixed Point Index

PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT

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Acta Mathematica Scientia 2014年第3期34卷 703-712页

作者：蓝永艺唐春雷 School of Mathematics and Statistics Southwest University School of Sciences Jimei University

In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation me... 详细信息

关键词： Critical Hardy-Sobolev exponent semilinear elliptic equation perturbation methods positive radial solution

EXISTENCE AND MULTIPLICITY OF positive solutionS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL

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Acta Mathematica Scientia 2006年第1期26卷 125-133页

作者：汪全珍陈祖墀 Department of Mathematics University of Science and Technology of China

By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f（t, u） increases in u.

关键词： Quasilinear positive radial solution multiplicity iteration