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RADIALLY SYMMETRIC SOLUTIONS FOR quasilinear elliptic equations INVOLVING NONHOMOGENEOUS OPERATORS IN AN ORLICZ-SOBOLEV SPACE SETTING

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Acta Mathematica Scientia 2020年第6期40卷 1679-1699页

作者： Jae-Myoung KIM Yun-Ho KIM Jongrak LEE Department of Mathematics Education Andong National UniversityAndong 36729Republic of Korea Department of Mathematics Education Sangmyung UniversitySeoul 03016Republic of Korea Department of Mathematics Jeju National UniversityJeju 63243Republic of Korea

We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1 详细信息

We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1

关键词： radial solution quasilinear elliptic equations variational methods Orlicz-Sobolev spaces

Existence of Three Solutions for quasilinear elliptic equations: an Orlicz-Sobolev Space Setting

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 287-296页

作者： Fei FANG Zhong TAN Department of Mathematics Beijing Technology and Business University School of Mathematical Sciences Xiamen University

In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].

关键词： Orlicz-Sobolev spaces quasilinear elliptic equations three critical points theorem

GRADIENT ESTIMATES FOR SOLUTIONS TO quasilinear elliptic equations WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL

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Acta Mathematica Scientia 2017年第1期37卷 58-68页

作者：向长林 Department of Mathematics and Statistics University of JyvaskylaP.O.Box 35FI-40014 University of JyvaskylaFinland

This note is a continuation of the work[17].We study the following quasilinear elliptic equations- △pu-μ/｜x｜p ｜u｜p-2 u=Q（x）｜u｜Np/N-p -2u,x∈R N,where 1 〈 p 〈 N,0 ≤ μ 〈（（N-p）/p）p and Q ∈ L∞（RN）.O... 详细信息

关键词： quasilinear elliptic equations Hardy＇s inequality gradient estimate

POSITIVE SOLUTIONS FOR CRITICAL quasilinear elliptic equations WITH MIXED DIRICHLET-NEUMANN BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2013年第2期33卷 443-470页

作者：丁凌唐春雷 School of Mathematics and Statistics Southwest University School of Mathematics and Computer Science Hubei University of Arts and Science Institute of Applied Physics and Computational Mathematics of Beijing

The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational... 详细信息

关键词： Mixed Dirichlet-Neumann boundary quasilinear elliptic equations Sobolev critical exponents Ekeland＇s variational principle Mountain Pass Lemma

BMO Estimates for quasilinear elliptic equations with BMO Coefficients

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Journal of Mathematical Research with Applications 2016年第6期36卷 673-681页

作者： Qiaoyu TIAN Shengzhi ZHANG Yonglin XU Jia MU School of Mathematics and Computer Science Northwest University for Nationalities Department of Mathematics Gansu Normal University for Nationalities

We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A(x,Du) = div(|F|F) under the BMO smallness of the nonlinearity,that is |F|F∈BMO implies that Du ∈BMO.

关键词： Calderón-Zygmund theory quasilinear elliptic equations BMO space

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME quasilinear elliptic equationsIN ANNULAR OMAINS

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Applied Mathematics(A Journal of Chinese Universities) 1999年第3期14卷 313-320页

作者： ZhangHui GuoZongming Dept.ofMath. HenanNormalUniv.Xinxiang453002. InstituteofSystemsScience AcademiaSinicaBeijing100080.

The existence ofpositive radialsolutions ofthe equation - div(｜Du｜p- 2Du)= f(u) is studied in annular dom ains in Rn,n≥2. Itisproved thatiff(0)≥0, f is somewhere negativein (0,∞), lim u→0+ f′(u)= 0and lim u→∞(f(u)/up- 1)= ∞, then thereisa largepositiveradialsolution on allannuli.Iff(0)< 0 and satisfiescertain condi- tions, then the equation has no radialsolution ifthe annuliare too wide.

关键词： quasilinear elliptic equations large solutions,positive radialsolutions,annular dom ains

Multiple Sign-Changing Solutions for quasilinear equations of Bounded quasilinearity

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Analysis in Theory and Applications 2021年第2期37卷 209-229页

作者： Jiaquan Liu Xiangqing Liu Zhi-Qiang Wang LMAM School of Mathematical SciencePeking UniversityBeijing 100871China Department of Mathematics Yunnan Normal UniversityKunmingYunnan 650500China College of Mathematics and Informatics and Center for Applied Mathematics of Fujian Province(FJNU) Fujian Normal UniversityFuzhouFujian 350117China Department of Mathematics and Statistics Utah State UniversityLoganUT 84322USA

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where Ω∈ C RN is a bounded domain with smooth boundary,and we use du 2u d D;u=x,Dju=;dxjdxj and D2bj;(z)=;bj(2).The main interest of this paper is for the case of bounded quasilinearity bj.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.

关键词： quasilinear elliptic equations sign-changing solution an elliptic regularization method

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO quasilinear SCHRDINGER equations

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Acta Mathematica Scientia 2016年第1期36卷 73-86页

作者：李周欣沈尧天 School of Mathematics and Statistics Central South University Changsha 400083 China Department of Mathematics South China University of Technology Guangzhou 510640 China

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equatio... 详细信息

关键词： nonsmooth critical point theorems quasilinear elliptic equations SchrSdingerequation

SOLUTIONS TO NONLINEAR elliptic equations WITH A GRADIENT

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Acta Mathematica Scientia 2015年第5期35卷 1023-1036页

作者：王影王明新 School of Mathematics and Information Science North China University of Water Resources and Electric Power Natural Science Research Center Harbin Institute of Technology

In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.

关键词： quasilinear elliptic equations existence and nonexistence gradient terms singular weights