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Existence of Solutions to Nonlinear Neumann Boundary Value problems with p-Laplacian Operator and Iterative Construction

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 463-470页

作者： Li Wei Hai-yun Zhou Ravi p. agarwal School of Mathematics and Statistics Hebei University of Economics and Business Shijiazhuang 050061 China Institute of Applied Mathematics Ordnance Engineering College Shijiazhuang 050003 China Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 U.S.A.

By using some results of pseudo-monotone operator, we discuss the existence and uniqueness of the solution of one kind nonlinear Neumann boundary value problems involving the p-Laplacian operator. We also construct an... 详细信息

关键词： maximal monotone operator pseudo-monotone operator p-Laplacian operator iterative scheme

An Upper and Lower Solution Theory for the problem(G′(y))′+f(t,y)=0 on Finite and Infinite Intervals

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Acta Mathematica Sinica,English Series 2006年第3期22卷 827-832页

作者： Ravi p.agarwal Donal O'REGAN Svatoslav STANEK Department of Mathematical Sciences Florida Institute of TechnologyMelbourneFlorida 32901-6975USA Department of Mathematics National University of IrelandGalwayIreland Department of Mathematical Analysis Faculty of SciencePalack University

A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,... 详细信息

关键词： alternative upper and lower solutions infinite interval diagonalization process Leray-Schauder alternative

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

positive Solutions to Singular Boundary Value problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1447-1456页

作者： Bao Qiang YAN Donal O'REGAN Ravi p. agarwal Department of Mathematics Shandong Normal University Ji'nan 250014 P. R. China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne FL32901 USA

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.

关键词： boundary value problems lower and upper solutions Schauder's fixed point theorem

Nonexistence and Existence of Multiple positive Solutions for Superlinear Three-point Boundary Value problems via Index Theory

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 529-540页

作者： Bao-qiang Yan Donal O'Regan Ravi p. agarwal Department of Mathematics Shandong Normal University Jinan 250014 China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne Florida 32901 USA

This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.

关键词： Three-point boundary value problems cone fixed point index

FDTD technique based crosstalk analysis of bundled SWCNT interconnects

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Journal of Semiconductors 2015年第5期36卷 90-98页

作者： Yograj Singh Duksh Brajesh Kumar Kaushik Rajendra p.agarwal Department of Electronics and Instrumentation Engineering Mahatma Jyotiba Phule Rohilkhand University Department of Electronics and Communication Engineering Indian Institute of Technology Shobhit University

The equivalent electrical circuit model of a bundled single-walled carbon nanotube based distributed RLC interconnects is employed for the crosstalk analysis. The accurate time domain analysis and crosstalk effect in the VLSI interconnect has emerged as an essential design criteria. This paper presents a brief description of the numerical method based finite difference time domain （FDTD） technique that is intended for estimation of voltages and currents on coupled transmission lines. For the FDTD implementation, the stability of the proposed model is strictly restricted by the Courant condition. This method is used for the estimation of crosstalk induced propagation delay and peak voltage in lossy RLC interconnects. Both functional and dynamic crosstalk effects are analyzed in the coupled transmission line. The effect of line resistance on crosstalk induced delay, and peak voltage under dynamic and functional crosstalk is also evaluated. The FDTD analysis and the SpICE simulations are carried out at 32 nm technology node for the global interconnects. It is observed that the analytical results obtained using the FDTD technique are in good agreement with the SpICE simulation results. The crosstalk induced delay, propagation delay, and peak voltage obtained using the FDTD technique shows average errors of 4.9%, 3.4% and 0.46%, respectively, in comparison to SpICE.

关键词： FDTD SWCNT bundle interconnects crosstalk delay peak voltage coupled transmission lines

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

Oscillation of fourth-order delay dynamic equations

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Science China Mathematics 2015年第1期58卷 143-160页

作者： ZHANG Cheng Hui agarwal Ravi p. BOHNER Martin LI Tong Xing School of Control Science and Engineering Shandong University Department of Mathematics Texas A&M University-Kingsville 700 University Blvd.Kingsville TX 78363-8202 USA Department of Mathematics and Statistics Missouri University of Science and TechnologyRolla MO 65409-0020 USA Department of Mathematics Linyi University

This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time *** the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to *** results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time *** criteria improve a number of related contributions to the *** illustrative examples are provided.

关键词： Swift-Hohenberg equation oscillation delay dynamic equation fourth-order time scale