examples of nonlinear first order differential equations

... solutions), unfortunately often identified in the literature on lower and upper solutions. First- order differential equations with state-dependent deviated argu- ments have received a lot of attention in ... compact set of fixed points in C(I), which are exactly the solutions of problem (4). Claim 2: Every solution x of (4) satisfies α ≤ x ≤ β on I and, therefore, it is a solution of (1) in [α, β]. First, ... [2–7] which deal with existence results for this kind of prob- lems. For the qualitative study of this type of problems we can cite the survey of Hartung et al. [8] and references therein. As main...

Ngày tải lên: 20/06/2014, 20:20

... the solvability of nonlinear singular equations subject to different types of boundary conditions. In this section, we utilize Theorem 4.1 to show the existence of solutions for periodic problems. The rest of ... Article Limit Properties of Solutions of Singular Second -Order Differential Equations Irena Rach ˚ unkov ´ a, 1 Svatoslav Stan ek, 1 Ewa Weinm ă uller, 2 and Michael Zenz 2 1 Department of Mathematical ... values of the first derivative at the end points of the interval of integration, t  0andt  1. According to the theory, it holds that u  0u  1 0. Therefore, we approximate the values of the...

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... a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei He (hexiaofei525@sina.com) ISSN ... for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R. China 2 College of Mathematics ... of Lyapunov. Am. J. Math. 73, 885–890 (1951) [3] Cheng, SS: Lyapunov inequalities for differential and difference equations. Fasc. Math. 23, 25–41 (1991) [4] He, Z: Existence of two solutions of...

Ngày tải lên: 20/06/2014, 21:20

... Walter W: On some nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first- order impulsive differential equations with ... non-linear differential equations of fractional order. Nonlinear Anal 2011, 74:792-804. 34. Zhang L, Wang G: Existence of solutions for nonlinear fractional differential equations with impulses ... solutions) of three-point BVPs for nonlinear inte- ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto [2-13] and the references therein. Fractional differential equations...

Ngày tải lên: 21/06/2014, 03:20

... delay dynamic equations of first order, ” Advances in Difference Equations, vol. 2008, Article ID 458687, 12 pages, 2008. 10 H. A. Agwo, “On the oscillation of first order delay dynamic equations with ... Article Nonoscillation of First- Order Dynamic Equations with Several Delays Elena Braverman 1 and Basáak Karpuz 2 1 Department of Mathematics and Statistics, University of Calgary, 2500 University ... uniqueness of solutions to systems of delay dynamic equations on time scales,” http://arxiv.org/abs/1001.0737v3 . 6 M. Bohner, “Some oscillation criteria for first order delay dynamic equations, ”...

Ngày tải lên: 21/06/2014, 11:20

... 2008.  13 B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher- order nonlinear fractional differential equations, ” Abstract and Applied Analysis, vol. ... Conclusions This paper studies the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary conditions ... Corporation Advances in Difference Equations Volume 2010, Article ID 691721, 10 pages doi:10.1155/2010/691721 Research Article Existence of Solutions for Nonlinear Fractional Integro -Differential Equations with...

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... some results of one and two positive solutions to a class of nonlinear first -order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two examples are ... for first order periodic boundary value problem. Appl. Math. Comput. 158, 345–351 (2004) [39] Sun, JP, Li, WT: Positive solution for system of nonlinear first -order PBVPs on time scales. Nonlinear ... available soon. Periodic boundary value problems for nonlinear first- order impulsive dynamic equations on time scales Advances in Difference Equations 2012, 2012:12 doi:10.1186/1687-1847-2012-12 Da-Bin...

Ngày tải lên: 21/06/2014, 17:20

... Solutions of Singular Nonautonomous Second -Order Differential Equations Irena Rach ˚ unkov ´ aandJanTome ˇ cek Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palack ´ y ... here we prove the existence of a homoclinic solution for f having a linear behaviour near −∞. The proof is based on a full description of the set of all solutions of problem 1.1, 1.10 for ... Problems 15 Proof. Similar arugmets can be found in 12.ByLemma 2.1, the assertion i holds. The arguments in Step 1 of the proof of Lemma 4.6 imply ii. The strict monotonicity of u n and Remark...

Ngày tải lên: 21/06/2014, 20:20

... Positive Solutions for Nonlinear First- Order Impulsive Dynamic Equations on Time Scales with Parameter Da-Bin Wang and Wen Guan Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, ... Leggett-Williams fixed point theorem, the existence of three positive solutions to a class of nonlinear first -order periodic b oundary value problems of impulsive dynamic equations on time scales with parameter ... Journal of Qualitative Theory of Differential Equations, vol. 2005, no. 12, pp. 1–22, 2005. 21 M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “On first order impulsive dynamic equations...

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Ngày tải lên: 23/06/2014, 00:20

... in study of stability of differential equations. By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations NFDEs and nonlinear ... “Dissipativity of θ-methods for nonlinear Volterra delay-integro-differential equations, ” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 898–907, 2007. Journal of Inequalities ... inequality to discuss the stability of nonlinear neutral functional differential equations NFDEs and a class of nonlinear neutral delay integrodifferential equations NDIDEs. 2. Generalized Halanay...

Ngày tải lên: 21/06/2014, 07:20

... result concerning the global structure of the set of positive solutions of parameterized nonlinear operator equations, which is essentially a consequence of Dancer 12, Theorem 2. Suppose that ... P. J. Torres, “Existence of one-signed periodic solutions of some second -order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, ... existence of one-sign solutions of the nonlinear problem x   f  t, x  ,t∈  0,T  , x  0   x  T  ,x   0   x   T  . 1.18 The proofs of the main results are based on the properties of...

Ngày tải lên: 21/06/2014, 11:20

... a third -order three-point boundary-value problem,” Electronic Journal of Differential Equations, vol. 2008, no. 99, pp. 1–10, 2008. 15 Q. Yao, “Positive solutions of singular third -order three-point ... sign-changing nonlinearity on time scales,” Electronic Journal of Differential Equations, vol. 2007, no. 19, pp. 1–12, 2007. 19 J. R. Graef and B. Yang, “Positive solutions of a third order nonlocal ... Article Monotone Positive Solution of Nonlinear Third -Order BVP with Integral Boundary Conditions Jian-Ping Sun and Hai-Bao Li Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou,...

Ngày tải lên: 21/06/2014, 11:20

... and Delay Higher -Order Differential Equations on Time Scales Liang-Gen Hu, 1 Ti-Jun Xiao, 2 and Jin Liang 3 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, ... existence of positive solutions. The purpose of this paper is to investigate further the singular BVP for delay higher- order dynamic equation 1.1. By the use of the fixed point theorem of cone ... value problems for delay higher -order dynamic equations on time scales. Theorems on the existence of positive solutions are obtained by utilizing the fixed point theorem of cone expansion and compression...

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