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EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF pARABOLIC p-LApLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

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Acta Mathematica Scientia 2016年第6期36卷 1780-1792页

作者：魏利陈蕊 ravi p.agarwal patricia YJ WONG School of Mathematics and Statistics Hebei University of Economics and Business Department of Mathematics Texas A&M University-Kingsville Department of Mathematics Faculty of ScienceKing Abdulaziz University School of Electrical and Electronic Engineering Nanyang Technological University

One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.

关键词： maximal monotone operator Caratheodory'conditions subdifferential p-Laplacian-tike equation nontrivial solution

ON A COUpLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

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Acta Mathematica Scientia 2021年第4期41卷 1366-1384页

作者： Bashir AHMAD ravi p.agarwal Abrar BROOM Ahmed ALSAEDI Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of Mathematics Texas A&M UniversityKingsvilleTexas 78363-8202USA

By applying the standard fixed point theorems,we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals,supplemented with nonlocal coupled fractional integral boundary *** example is also constructed for the illustration of the obtained results.

关键词： Fractional differential equations Caputo and Riemann-Liouville fractional derivatives systems existence fixed point theorems

Oscillation Theorems for Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales

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Acta Mathematica Sinica,English Series 2008年第9期24卷 5-1432,1410页

作者： Samir H.SAKER Donal O’REGAN ravi p.agarwal Department of Mathematics College of Science King Saud University Riyadh 11451 Saudi Arabia Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Sciences Florida Institute of Technology Melbourne Florida 32901 USA

By employing the generalized Riccati transformation technique,we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation [r(t)[y(t)+p(t)y(■(t))]~Δ]~Δ+q(t)f(y((δ(t)))=0 on a time scale■.The results improve some oscillation results for neutral delay dynamic equations and in the special case when■our results cover and improve the oscillation results for second- order neutral delay differential equations established by Li and Liu[***.,48(1996), 871 886].When■,our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh[***.,36(1998),123-132].When ■ ■our results are essentially *** examples illustrating our main results are given.

关键词： oscillation neutral delay dynamic equation generalized Riccati technique time scales

EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER DIFFERENTIAL DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2015年第5期35卷 1077-1094页

作者：郭承军 Donal O’REGAN 徐远通 ravi p.agarwal School of Applied Mathematics Guangdong University of Technology School of Mathematics Statistics and Applied Mathematics National University of Ireland Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group Department of Mathematics King Abdulaziz University Department of Mathematics Sun Yat-sen University Department of Mathematics Texas A and M University-Kingsville

In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.

关键词： homoclinic solutions differential difference equation critical point theory

含有广义p-Laplace算子的抛物边值问题解的存在性

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应用数学学报 2014年第1期37卷 1-12页

作者：魏利 ravi p.agarwal 河北经贸大学数学与统计学学院石家庄050061 Department of Mathematics Texas Agricultural and Mechanical University-KingsvilleTexasusatx783638202

利用极大单调单调算子值域的扰动结论,借助于构造辅助方程的技巧,研究了一类含有广义p-Laplace算子且具有混合边值条件的非线性抛物方程,并得到了这类非线性边值问题解的存在性的抽象结论.文中所用方法是对以往工作的推广和补充.

关键词：极大单调算子 hemi连续映射广义p-Laplace算子值域的和非线性抛物边值问题

SUMUDU TRANSFORM IN BICOMpLEX SpACE AND ITS AppLICATIONS

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Annals of Applied Mathematics 2017年第3期33卷 239-253页

作者： Ritu agarwal Mahesh puri Goswami ravi p.agarwal Dept.of Math. Malaviya National Institute of TechnologyJaipur-302017India Dept.of Math. Texas A&M University-Kingsville 700 University Blvd.KingsvilleTX 78363-8202USA

In this paper, we define Sumudu transform with convergence conditions in bicomplex space. Also, we derive some of its basic properties and its inverse. Applications of bicomplex Sumudu transform are illustrated to find the solution of differential equation of bicomplex-valued functions and find the solution for Cartesian transverse electric magnetic （TEM） waves in homogeneous space.

关键词： Sumudu transform bicomplex numbers bicomplex functionsand bicomplex Laplace transform

非线性椭圆边值问题和极大单调算子的零点(英文)

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应用数学 2013年第2期26卷 371-379页

作者：魏利樊树新 ravi p.agarwal 河北经贸大学数学与统计学学院河北石家庄050061 Department of Mathematics Texas Agricultural and Mechanical University-Kingsvilles

本文利用非线性极大单调算子值域的扰动结论,研究一类与广义p-Laplacian算子相关的、具Neumann边值条件的非线性椭圆方程的解的存在唯一性.同时研究这个唯一解与适当定义的非线性极大单调算子的零点之间的关系.进而设计一种迭代算法强... 详细信息

本文利用非线性极大单调算子值域的扰动结论,研究一类与广义p-Laplacian算子相关的、具Neumann边值条件的非线性椭圆方程的解的存在唯一性.同时研究这个唯一解与适当定义的非线性极大单调算子的零点之间的关系.进而设计一种迭代算法强收敛到这个唯一解本文采用新的构造算子和拆分方程的方法。

关键词：单调算子零点广义p-Laplacian算子 Caratheodory条件非线性椭圆边值问题

H增生映射和含有广义(p,q)-Laplacian算子的非线性椭圆系统

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应用数学学报 2018年第5期41卷 653-666页

作者：魏利张瑞兰 ravi p.agarwal 河北经贸大学数学与统计学学院石家庄050061 Department of Mathematics Texas A & M University -Kingsville Kingsville TX 78363 USA Distinguished University professor of Mathematics Florida Institute of Technology Melbourne FL 32901 USA

利用H增生映射的性质,证明了含有广义（p,q）-Laplacian算子的非线性椭圆系统存在唯一解的结论.证明方法简单且研究结果展示了H增生映射和非线性椭圆系统之间的关系,推广和补充了以往的相关研究工作.

关键词： H增生映射极大单调算子 (p,q)-Laplacian算子非线性椭圆系统

含有广义p-Laplace算子具混合边值条件的积分微分方程解的存在唯一性(英文)

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数学杂志 2013年第6期33卷 1009-1018页

作者：魏利段丽凌 ravi p.agarwal 河北经贸大学数学与统计学学院河北石家庄050061 Department of Mathematics Texas Agricultural and Mechanical University-Kingsville

本文研究了一类含有广义p-Laplace算子、具有混合边值条件的积分微分方程.运用将积分微分方程分解为非线性算子的研究方法,获得了这类方程解的存在唯一性的结论.与以往相关工作相比,不仅得到了解的存在性,还证明了解的唯一性.同时摒弃... 详细信息

本文研究了一类含有广义p-Laplace算子、具有混合边值条件的积分微分方程.运用将积分微分方程分解为非线性算子的研究方法,获得了这类方程解的存在唯一性的结论.与以往相关工作相比,不仅得到了解的存在性,还证明了解的唯一性.同时摒弃了传统的有限元法,而改用极大单调算子和伪压缩算子的值域理论研究问题,从而推广和补充了以往的研究工作.

关键词：极大单调算子伪单调算子广义p-拉普拉斯算子具有混合边值条件的积分微分方程