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Uniqueness and Radial Symmetry of Least Energy Solution for a Semilinear Neumann Problem

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 473-482页

作者： Zheng-ping Wang Huan-song Zhou Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences P.O.Box 71010 Wuhan 430071 China

Consider the following Neumann problem d△u- u ＋ k（x）u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,where d 〉 0, B1 is the unit ball in R^N, k（x） = k（｜x｜） ≠ 0 is nonnegative and in C（-↑B1）, 1 〈 p 〈 N＋2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem （＊） has no nonconstant radially symmetric least energy solution if k（x） ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that （＊） has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k（x） ≡ 1 and nonconstant if k（x） ≠ 1. In particular, for k（x） ≡ 1, do can be expressed explicitly.

关键词： implicit function theorem least energy solution radial symmetry Neumann problem elliptic

Dependence of eigenvalues of regular Sturm- Liouville operators on the boundary condition

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Frontiers of Mathematics in China 2023年第1期18卷 63-74页

作者： Xinya YANG School of Mathematics and Statistics Shaanxi Normal UniversityXi'an 710119China Shanxi Engineering Vocational College Taiyuan 030009China

In this paper,we study the continuous dependence of eigenvalue of Sturm-Liouville differential operators on the boundary condition by using of implicit function *** work not only provides a new and elementary proof of the above results,but also explicitly presents the expressions for derivatives of the n-th eigenvalue with respect to given ***-more,we obtain the new results of the position and number of the generated double eigenvalues under the real coupled boundary condition.

关键词： Regular Sturm-Liouville operator eigenvalue implicit function theorem

ONE-SIDED N-WIDTHS OF SOME CLASSES OF PERIODIC functionS

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Analysis in Theory and Applications 1993年第4期9卷 21-36页

作者： Fang Gensun Zhang Jianhua Beijing Normal University,China Department of Mathematics Beijing Normal University Beijing PRC

In this paper,we determine the exact estimation of one-sided n-widths d_n^+(w_q^r(p_r),L_1).q=1,∝, where W_q^r(P_r)is a class of differentiable 2π-periodic functions,and is determined by a differential opera- tor P_... 详细信息

关键词： Differential Operator Periodic function implicit function theorem Simple Zero Exact Estimation

Remarks on a Mathematical Model from the Theory of Optimal Investment

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Northeastern Mathematical Journal 2001年第2期17卷 127-129页

作者：廉松哲王光烈陈丽伍卓群 Department of Mathematics Jilin University Changchun 130023

In Chapter 4 of [1], from the theory of optimal investment in mathematical finance, the following initial value problem for a parabolic Monge-Ampère equation was derived:

关键词： Hamilton Jacobi Bellman equation parabolic Monge Ampère equation implicit function theorem

Positive Solutions for a Class of Quasilinear Schrödinger Equations with Nonlocal Term

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Journal of Applied Mathematics and Physics 2022年第2期10卷 347-359页

作者： Peng Liao Rui Ping Shaoxiong Chen School of Mathematics Yunnan Normal University Kunming China

This paper is considered the existence of positive solutions for a class of generalized quasilinear Schrödinger equations with nonlocal term in RN which have appeared from plasma physics, as well as high-power ultrash... 详细信息

关键词： Quasilinear Schrödinger Equation Minimization implicit function theorem