existence of global solutions and attractors

... Theory of Functions and Almost Periodicity 2.1 Notations In the remaining part of this paper we will use the following notations: C, and z stand for the set of complex numbers and the real part of ... MAN AND NGUYEN VAN MINH countable, where Sp(f ) is the Beurling spectrum of f , that is equal to the closure of the set of the Fourier exponents of f in the case of almost periodic functions, and ... uniformly continuous solution of Eq (1.1) Then SpAP (x) ⊂ ∆i QUASI PERIODIC AND ALMOST PERIODIC SOLUTIONS 295 Proof Taking Carleman transforms of both sides of (1.1) and applying Fubini Theorem,

Ngày tải lên: 16/12/2017, 16:50

... Positive solutions of nonlinear singular third-order two-point boundary value problem J Math Anal Appl 323, 413-425 (2006) 12 Graef, JR, Yang, B: Existence and nonexistence of positive solutions of ... solutions by the Krasnoselskii and Leggett-Williams fixed point theorems Liang and Zhang [] investigated the existence and uniqueness of positive and nondecreasing solutions by using a fixed point ... = v and v = Tv Thus, w and v are two nonnegative solutions of problem () Because the zero function is not a solution of problem (), we have max≤t≤ |w(t)| >  and max≤t≤ |v(t)| > , and

Ngày tải lên: 24/11/2022, 17:57

... will discuss the causes and effects of global warming and give some possible solutions Global warming is the increase of Earth's average surface temperature due to effect of greenhouse gases, such ... more and more severe The essay will discuss the problem of global warming, its causes and effects and suggest some solutions for it Global warming is the rise in the average temperature of the ... because of the amount of packaging used and the short life cycle of products A lot of items, waste and packaging isn't recyclable, which means it ends up in landfills When the waste in landfills

Ngày tải lên: 11/01/2023, 17:24

... (1.2), and obtain the existence of positive solutions of (1.1) and (1.2). More- over, we can also obtain the existence of negative solutions of (1.1) and (1.2). Now, we give the definition of a ... solution and a negative solution of (1.1) and (1.2). Definition 1.1. A positive solution of problem (1.1) and (1.2) refers to a pair (r, u), where r ≠ 0, u is a solution of (1.1) with u >0on T and ... isacharacteristicvalueofT if there exists v Î E, v ≠ 0, such that v = μTv,i.e.,μ -1 is a nonz ero eigenvalue of T. Let r(T) denote the set of real characte ristic values of T and Γ denote the closure of the set of

Ngày tải lên: 20/06/2014, 20:20

... lies between 100 and 1000 Existence of at least two positive solutions In this section, we will apply fixed point Theorem 2.5 to prove the existence of at least two positive solutions to the nonlinear ... value problems of ordinary differential equations (BVPs for short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform ... section and composed of N parts of different densities can be set up as a multi-point boundary value problem [3] Many problems in the theory of elastic stability can be handled by the method of multi-point

Ngày tải lên: 20/06/2014, 20:20

... Article Existence of Positive Solutions for Multipoint Boundary Value Problem with p-Laplacian on Time Scales Meng Zhang, 1 Shurong Sun, 1 and Zhenlai Han 1, 2 1 School of Science, University of Jinan, ... 1, or 2 and there are six possible cases: i i 0  0andi ∞  0; ii i 0  0andi ∞  1; iii i 0  0andi ∞  2; 8 Advances in Difference Equations iv i 0  1andi ∞  0; v i 0  1andi ∞  ... School of Science, University of Jinan, Jinan, Shandong 250022, China 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China Correspondence should be addressed

Ngày tải lên: 21/06/2014, 20:20

... 4, we study the existence of weak solutions to Problem 1. Using Rothe’s method of time discretization and an existence result for Problem 1,one can establish existence of week solutions to the ... H 1,r 0 Ω  p 0 to 3.1 in the sense of Definition 3.1. Proof of Theorem 3.2. The existence result is given in Corollary 3.5, and we now turn to proof of uniqueness. For a given θ, assume that ... Article Existence of Weak Solutions for a Nonlinear Elliptic System Ming Fang 1 and Robert P. Gilbert 2 1 Department of Mathematics, Norfolk State University, Norfolk, VA 23504, USA 2 Department of

Ngày tải lên: 21/06/2014, 20:20

... introduced by Kaplan and Yorke in to reduce the search for periodic solutions of 1.2 with n and its similar ones to the problem of finding periodic solutions for a related system of ordinary differential ... ψ x ,y ν f t, x t , y t dt 2.21 Our aim is to reduce the existence of periodic solutions of 2.12 to the existence of critical points of φ For this we introduce a shift operator Γ : H → H defined ... Analysis and Applications, vol 5, no 3, pp 435–450, 1962 S.-N Chow and H.-O Walther, “Characteristic multipliers and stability of symmetric periodic solutions of x ˙ g x t − ,” Transactions of the

Ngày tải lên: 21/06/2014, 20:20

... obtained the existence of at least double and triple positive solutions of the problems by using a new double fixed point theorem and triple fixed point theorem, respectively In 18 , Zhou and Ma firstly ... Results We now give our results on the existence of positive solutions of BVP 1.6 Theorem 3.1 Suppose that conditions H1 and H2 hold, and assume that one of the following conditions holds H3 There ... The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales Fuyi Xu and Zhaowei Meng School of Science, Shandong

Ngày tải lên: 21/06/2014, 20:20

... Science, University of Jinan, Jinan, Shandong 250022, China 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China 3 Department of Mathematics and Statistics, ... operators U and S as in Theorem 2.3 with p replaced by p 1 . The rest of the proof is similar to that of Theorem 2.3 and hence omitted. The proof is complete. Theorem 2.5. Assume that H holds and −1 ... subset of the reals. The motivation originates from Kulenovi ´ c and Had ˇ ziomerpahi ´ c 23 and Zhu and Wang 24.In23, the authors established some sufficient conditions for the existence of

Ngày tải lên: 21/06/2014, 20:20

... point theory. Inspired and motivated by Jiang and Zhou 10, Nieto and O’Regan 20, and Zhang and Li 21,westudy the existence of weak solutions for boundary value problems of impulsive dynamic ... and nonlinear alternative of Leray-Schauder type. However, to the best of our knowledge, few papers have been published on the existence of solutions for second-order boundary value problem of ... doi:10.1155/2009/907368 Research Article Existence of Weak Solutions for Second-Order Boundary Value Problem of Impulsive Dynamic Equations on Time Scales Hongbo Duan and Hui Fang Department of Applied Mathematics,

Ngày tải lên: 21/06/2014, 20:20

... theorem of coincidence degree theory 3. The author obtained a new result for the existence of periodic solutions and investigated the relation between the existence of periodic solutions and the ... China 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China 3 Department of Mathematics and Statistics, Missouri U niversity of Science and Technology, ... Article Existence of Periodic Solutions for p-Laplacian Equations on Time Scales Fengjuan Cao, 1 Zhenlai Han, 1, 2 and Shurong Sun 1, 3 1 School of Science, University of Jinan, Jinan, Shandong

Ngày tải lên: 21/06/2014, 20:20

... and K Mukai, Existence and nonexistence of global solutions to fast diffusions with source,” Methods and Applications of Analysis, vol 2, no 1, pp 92–102, 1995 R G Pinsky, Existence and nonexistence ... Suzuki, 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 ... discussions and friendly encouragement 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...

Ngày tải lên: 21/06/2014, 11:20

... Zheng and Q Zhang, Existence and multiplicity of solutions of second-order difference boundary value problems,” Acta Applicandae Mathematicae, vol 110, no 1, pp 131–152, 2010 X Cai and J Yu, Existence ... − , and < V t ≤ γ < λk , then 1.1 has at least five solutions Moreover, one of the following cases occurs: i k is even and 1.1 has two sign-changing solutions, ii k is even and 1.1 has six solutions, ... and 1.1 has six solutions, three of which are of the same sign, iii k is odd and 1.1 has two sigh-changing solutions, iv k is odd and 1.1 has three solutions of the same sign Remark 1.4 The assumption...

Ngày tải lên: 21/06/2014, 05:20

... 2.78 and H r, t → as r → ∞ Then 2.77 implies 2.58 and the proof of Lemma 2.12 is completed Remark 2.13 In fact, we see from the proof of Lemma 2.12 that if 2.73 and 2.76 are satisfied, then 2.77 and ... obtain the continuity of solution of 1.1 - 1.2 in Lp RN , p ≥ 2, we derive L∞ estimate of solutions by Moser’s technique as in 4, 6, We will prove that the existence of the global attractor Ap ... with local and nonlocal nonlinearity,” Journal of Mathematical Analysis and Applications, vol 337, no 1, pp 318–332, 2008 Boundary Value Problems 17 M Nakao and C Chen, Global existence and gradient...

Ngày tải lên: 21/06/2014, 20:20

... virtue of (3.46), (3.47), and (3.48) there exists the number T = T0 > for which the right-hand side of inequality (3.46) is negative, but this is impossible because the left-hand side of inequality ... [25] M Aassila, Global existence of solutions to a wave equation with damping and source terms, Differential Integral Equations 14 (2001), no 11, 1301–1314 E Belchev, M Kepka, and Z Zhou, Finite-time ... 29–51 F John and S Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, Comm Pure Appl Math 37 (1984), no 4, 443–455 T Kato, Blow-up of solutions of some nonlinear...

Ngày tải lên: 23/06/2014, 00:20

... differential equations of fractional order,” Journal of Applied Mathematics and Computing, vol 29, no 1-2, pp 125–135, 2009 16 C F Li, X N Luo, and Y Zhou, Existence of positive solutions of the boundary ... Foundation of University of South China under Grant no 5-XQD-2006-9, the Foundation of Science and Technology Department of Hunan Province under Grant no 2009RS3019 and the Subject Lead Foundation of ... basics of fractional derivative and the fixed point theorems which will be used in Section to establish the existence of positive solutions To conclude the paper, the feasibility of some of the...

Ngày tải lên: 21/06/2014, 05:20

... the solvability of 1.1 and present the existence of mild solution of 1.1 based on Kuratowski’s measures of noncompactness Moreover, an example is presented to show an application of the abstract ... integrodifferential equations,” Dynamics of Continuous, Discrete & Impulsive Systems Series A, vol 15, no 6, pp 815–824, 2008 10 T.-J Xiao and J Liang, “Blow-up and global existence of solutions to integral equations ... spaces,” International Journal of Mathematics and Mathematical Sciences, vol 14, no 3, pp 497–508, 1991 14 G M Mophou and G M N’Gu´ r´ kata, Existence of mild solutions of some semilinear neutral...

Ngày tải lên: 21/06/2014, 05:20

... L Yao and Z B Bai, Existence of positive solutions of a BVP for u4 t − λh t f u t 0,” Chinese Annals of Mathematics Series A, vol 20, no 5, pp 575–578, 1999 14 Q Yao, “Local existence of multiple ... no 11026060 , and nwnu-kjcxgc03-69, 03-61 References Z Bai, “The method of lower and upper solutions for a bending of an elastic beam equation,” Journal of Mathematical Analysis and Applications, ... 6, pp 1069–1078, 2003 X.-L Liu and W.-T Li, Existence and multiplicity of solutions for fourth-order boundary value problems with three parameters,” Mathematical and Computer Modelling, vol 46,...

Ngày tải lên: 21/06/2014, 07:20

... papers 1–3, 11–14 , the authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of 1.1 by using the critical point theory These ... homoclinic solution of 1.1 The proof is complete Proof of Corollary 1.5 Obviously, F7 and F8 imply that F4 holds, and F7 and F9 imply a2 n b n |a n | In addition, by F7 and F8 , we have that ... 10771215 of China and supported by the Outstanding Doctor degree thesis Implantation Foundation of Central South University no: 2010ybfz073 References Z Guo and J Yu, Existence of periodic and subharmonic...

Ngày tải lên: 21/06/2014, 11:20