lie groups singularities and solutions of nonlinear partial differential equations

... 105–116, 1989 Y Song and H Tian, “Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay,” Journal of Computational and Applied Mathematics, vol ... almost periodic solutions of nonlinear Volterra difference equations with unbounded delay,” Journal of Difference Equations and Applications, vol 14, no 9, pp 971–986, 2008 S K Choi and N J Koo, “Asymptotic ... Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Mathematical Sciences, vol 14, Springer, New York, NY, USA, 1975 C Zhang, Almost Periodic Type Functions and...

Ngày tải lên: 22/06/2014, 11:20

... Cheng and G Zhang, Positive periodic solutions of a discrete population model, Functional Differential Equations (2000), no 3-4, 223–230 [2] S Elaydi and S Zhang, Stability and periodicity of difference ... existence of periodic solutions of discrete difference equations, Uzbekski˘ ı Matematicheski˘ Zhurnal (1995), no 3, 88–90 (Russian) ı [10] Kh Turaev, On the existence and uniqueness of periodic solutions ... 241–248 [6] M I Gil’, S Kang, and G Zhang, Positive periodic solutions of abstract difference equations, Applied Mathematics E-Notes (2004), 54–58 [7] A Halanay, Solutions p´riodiques et presque-p´riodiques...

Ngày tải lên: 22/06/2014, 22:20

... conditions and obtain a closed form analytic solution of Equations (1) and (2) Choosing the parametric region to be ≤ u ≤ and ≤ v ≤ 2π, and assuming that the conditions given in Equations (3), (4) and ... patch of order 2N, we can specify two function conditions, as given in Equations (3) and (5), that should be satisfied at the edges (at u = and u = 1) of the surface patch, and a number of function ... measurement of the amount of oedema as well as the area and volume of the ulcer wounds This is because without an accurate and objective means of measuring changes in the size or shape of ulcers,...

Ngày tải lên: 13/08/2014, 23:20

... impulsive nonlinear Fredholm integral equations and applications,” Journal of Mathematical Analysis and Applications, vol 173, no 1, pp 318–324, 1993 D Guo and X Liu, “Multiple positive solutions of ... 3.2 ∀t ∈ J , and {xn t } and {xn t } converge uniformly to x t and x t on Ji , i 0, 1, 2, , respectively Proof By Lemma 2.3 and the definition of operator T , we have xn ⊂ P , and xn ≤ β α ... careful reading of the paper and useful suggestions References V Lakshmikantham, D D Ba˘nov, and P S Simeonov, Theory of Impulsive Differential Equations, vol ı of Series in Modern Applied Mathematics,...

Ngày tải lên: 21/06/2014, 11:20

... analogues of nonlinear implicit differential equations convergence of the explicit Euler method for nonlinear index-1 DAEs is established The results of this section are a nonlinear version” of the ... discrete analogues of nonlinear implicit differential equations Since condition (3.7) is independent of the choice of Q(t), the nonsingularity of G(x,t) does not depend on the choice of Q(t) For simplicity, ... discretization of nonlinear implicit differential equations is studied The compatibility between index notions for nonlinear index-1 DAEs and nonlinear index-1 IDEs as well as the convergence of the explicit...

Ngày tải lên: 22/06/2014, 22:20

... differentiability and applications to set differential equations, J Nonlinear Analysis Vol 61, pp 559- 575, (2005) [4] Lakshmikantham V; Set differential equations versus fuzzy differential equations, J Applied ... proof if we choose < δ ( ε ) ≤ ( K + 1) exp (C ) CONCLUSION In this paper we gave a new concept of set control differential equation and studied its existence of solutions A comparison of two solutions ... ] Some results on comparison of solutions of SDE and stability of solutions of SDE were studied in [1, 4, 5] MAIN RESULTS In this paper, we provide a set control differential equation (SCDE)...

Ngày tải lên: 22/07/2014, 06:20

... Introduction First-Order Partial Differential Equations 2.1 Linear Partial Differential Equations of First Order 2.2 Quasilinear Partial Differential Equations of First Order 2.3 Reduction of ut + un ux + ... = Exact Similarity Solutions of Nonlinear PDEs 3.1 Reduction of PDEs by Infinitesimal Transformations 3.2 Systems of Partial Differential Equations 3.3 Self-Similar Solutions of the Second Kind ... exact solutions of nonlinear problems for several decades I have also had the pleasure of association of a large number of students, postdoctoral fellows, and other colleagues, from both India and...

Ngày tải lên: 24/04/2014, 17:09

... doi:10.1002/mma.340 19 Han, XS, Wang, WM: Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source Nonlinear Anal 71, 5427–5450 (2009) doi:10.1016/j.na.2009.04.031 ... decay of solutions for a quaslinear system of viscoelastic equations Nonlinear Anal 71, 2257–2267 (2009) doi:10.1016/j.na.2009.01.060 22 Agre, K, Rammaha, MA: Systems of nonlinear wave equations ... damping and source terms Diff Integ Equ 19, 1235–1270 (2006) 23 Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a nonlinear system of viscoelastic wave equations Nonlinear...

Ngày tải lên: 21/06/2014, 00:20

... R Ma and N Castaneda, “Existence of solutions of nonlinear m-point boundary-value problems,” Journal of Mathematical Analysis and Applications, vol 256, no 2, pp 556–567, 2001 16 S Liang and J ... definitions and prove several preliminary results in Section Sections 3, 4, and are devoted to the existence of positive solutions of 1.1 and 1.2 , with the main tool being the AveryHenderson and Leggett-Williams ... solution of 2.6 and 2.7 The proof is complete Lemma 2.6 Assume that H1 holds, for h ∈ Cld 0, T and h ≥ 0, then the unique solution u of 2.6 and 2.7 satisfies u t ≥ 0, for t ∈ 0, T 2.12 Proof Let...

Ngày tải lên: 21/06/2014, 20:20

... Difference Equations and Inequalities, Monographs and Textbooks in Pure and Applied Mathematics, vol 155, Marcell Dekker, New York, 1992 S Bancroft, J K Hale, and D Sweet, Alternative problems for nonlinear ... Q is clearly linear, bounded, and maps onto Im(U), and that Q((I − E)x) = if and only if (I − E)x = 180 Periodic solutions of nonlinear second-order difference equations Remark 3.3 In the case ... require f (z) < and f (−z) > for all z > β, the conclusions of the theorem still hold We let ∆= 2kπ : k and j are integers, ≤ 2k < j and j is odd j (3.62) 186 Periodic solutions of nonlinear second-order...

Ngày tải lên: 23/06/2014, 00:20

... consist of two sets of equations: State equations, which describe the evolution of the states as a function of the input and state variables, being a set of time-dependent ordinary differential equations ... Printed and bound in the United States of America 69/3830-543210 Printed on acid-free paper SPIN 10868248 TLFeBook For God had not given us the spirit of fear; but of power, and of love, and of a ... and Director Professor Michael A Johnson, Professor of Control Systems and Deputy Director Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde,...

Ngày tải lên: 01/01/2014, 18:38

... procedure of the article, and explains some of the intuitions behind our formulation for the reader Definition of the problem We deal with the question of existence and uniqueness of solutions of nonlinear ... and the uniqueness of the deflection of an infinite beam resting on a both non-uniform and nonlinear elastic foundation by means of Banach fixed point theorem In fact, this restriction on the candidate ... Existence and uniqueness of nonlinear deflections of an infinite beam resting on a nonuniform nonlinear elastic foundation Sung Woo Choi1 and Taek Soo Jang∗2 Department of Mathematics, Duksung...

Ngày tải lên: 20/06/2014, 20:20

... “Existence and nonexistence of global solutions of quasilinear parabolic equations, ” Journal of the Mathematical Society of Japan, vol 54, no 4, pp 747–792, 2002 C Bandle, H A Levine, and Q S Zhang, ... during the preparation of this paper References P Baras and R Kersner, “Local and global solvability of a class of semilinear parabolic equations, ” Journal of Differential Equations, vol 68, no ... proof of Theorem 1.2 is included in the proof of Theorem 1.1 a In the following, R and T are two given positive real numbers greater than C is a positive constant independent of R and T , and...

Ngày tải lên: 21/06/2014, 11:20

... positive solutions of singular second-order equations and systems; see for instance Chu and Torres , Chu et al , Franco and Torres , Jiang et al , and Torres Moreover, the positiveness of Green’s ... study the existence of one-sign solutions of the nonlinear problem x f t, x , t ∈ 0, T , 1.18 x x T , x x T The proofs of the main results are based on the properties of G and the Dancer’s global ... existence of positive solutions of 3.17 will not be guaranteed in this case Proof of Theorem 3.2 We only prove i ii can be proved by a similar method To study the existence of positive solutions of...

Ngày tải lên: 21/06/2014, 11:20

... Problems the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandall et al had applications of Perron’s Method to second-order partial differential equations in ... Hamilton-Jacobi equations, ” Communications on Pure and Applied Analysis, vol 6, no 2, pp 389–410, 2007 D Nunziante, “Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations ... Differential and Integral Equations, vol 3, no 1, pp 77–91, 1990 D Nunziante, “Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence,” Nonlinear...

Ngày tải lên: 21/06/2014, 20:20

... procedure of the article, and explains some of the intuitions behind our formulation for the reader Definition of the problem We deal with the question of existence and uniqueness of solutions of nonlinear ... and the uniqueness of the deflection of an infinite beam resting on a both non-uniform and nonlinear elastic foundation by means of Banach fixed point theorem In fact, this restriction on the candidate ... Existence and uniqueness of nonlinear deflections of an infinite beam resting on a nonuniform nonlinear elastic foundation Sung Woo Choi1 and Taek Soo Jang∗2 Department of Mathematics, Duksung...

Ngày tải lên: 21/06/2014, 20:20

... conditions C1, C2, and C5 or C6 as in the result of Xu and Kim It is our purpose in this paper to modify the schemes 1.8 and 1.9 and prove strong convergence theorems for the unique solution of the variational ... Banach space and let K be a nonempty, closed, and convex subset of E Let P be a mapping of E onto K Then, P is said to be sunny if P P x t x − P x P x for all x ∈ E and t ≥ A mapping P of E into ... differentiable a and T : K → K is nonexpansive with F T / ∅, then F T is a nonexpansive retract of K Let K be a nonempty closed convex and bounded subset of a Banach space E and let the diameter of K be...

Ngày tải lên: 22/06/2014, 06:20

... Journal of Inequalities and Applications and weak solutions of the anisotropic equations −divA x, u , Du − N i ∂fi , ∂xi 1, q u ∈ Wloc i Ω 1.4 We refer to the classical books by Ladyˇ enskaya and ... Boccardo and Giachetti to the nonlinear case in For anisotropic cases, Giachetti and Porzio recently proved in the local Ls -summability for minima of anisotropic functionals and weak solutions of ... , and 1.10 that the integrand f and the operator A satisfy some growth conditions depending on u, in the proof of the local regularity results, we have to estimate the integral of some power of...

Ngày tải lên: 22/06/2014, 06:20