nonlinear second order differential equations examples

... pages doi:10.1155/2009/905769 Research 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 ... becoming finer. We finally observe experimentally the order of convergence of the numerical method collocation. Clearly, we do not expect very hight order to hold, since the analytical solution has ... in Theorems 4.1 and 4.2 constitute a useful tool when investigating the solvability of nonlinear singular equations subject to different types of boundary conditions. In this section, we utilize...

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... pages doi:10.1155/2009/959636 Research Article Homoclinic Solutions of Singular Nonautonomous Second- Order Differential Equations Irena Rach ˚ unkov ´ aandJanTome ˇ cek Department of Mathematical Analysis ... and second order differential equations with a singularity of the first kind,” Analysis, vol. 21, no. 4, pp. 373–389, 2001. 7 D. Bonheure, J. M. Gomes, and L. Sanchez, “Positive solutions of a second- order ... interfaces by second gradient theory: numerical simulations,” European Journal of Mechanics. B, vol. 15, no. 4, pp. 545–568, 1996. 2 G. H. Derrick, “Comments on nonlinear wave equations as models...

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... HO, Wu, J: Functional differential equations with state-dependent delays: theory and applications. Hand- b ook of Differential Equations: Ordinary Differential Equations, vol. III. Elsevier/North-Holland, ... text (HTML) versions will be made available soon. Minimal and maximal solutions to first -order differential equations with state-dependent deviated arguments Boundary Value Problems 2012, 2012:7 ... prove some new results on existence of solutions to first -order ordinary differential equations with deviated arguments. Delay differential equations are included in our general framework, which even...

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... certain higher -order differential equations. Appl. Math. Comput. 134(2–3), 307–317 (2003) [17] Cakmak, D: Lyapunov-type integral inequalities for certain higher order differential equations. Appl. ... (HTML) versions will be made available soon. Lyapunov-type inequalities for a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming ... for differential and difference equations. Fasc. Math. 23, 25–41 (1991) [4] He, Z: Existence of two solutions of m-point boundary value problem for second dy- namic equations on time scales. J....

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... boundary value problems for nonlinear differential equations. In: Fitzpertrick PM, Martelli M, Manhin J, Nussbaum R (eds.) Topological Method for Ordinary Differential Equations. Lecture Notes in Mathematics, ... integral equations arisen from nonlocal boundary- value problems. Elec J Differ Equ. 2002(30), 1–17 (2002) 24. Lomtatidze, A, Malaguti, L: On a nonlocal boundary value problem for second- order nonlinear ... problems with Riemann-Stieltjes Δ-integral conditions for second- order dynamic equations on time scales at resonance. Advances in Difference Equations 2011 2011:42. Submit your manuscript to a journal...

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... methods when we solve super- linear differential equations such as elliptic problems, Dirac equations, Hamiltonian systems, wave equations, and Schrödinger equations. Theorem 3.2. Assume that ... solutions for p(x)-Laplacian equations in ℝ N . Nonlinear Anal. 59, 173–188 (2004) 19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations. In CBMS Reg ... Neumann-type differential inclusion problem involving the p(x)-Laplacian. Nonlinear Anal. 70, 3755–3760 (2009). doi:10.1016/j.na.2008.07.031 4. Dai, G: Infinitely many solutions for a differential...

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... value problem for second order differential equations with an advanced argument. Nonlinear Anal 2006, 65:2013-2023. 42. Jankowski T: Positive solutions for fourth -order differential equations with ... 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 ... problem for 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...

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... sequences and second order difference equations, ” Journal of Difference Equations and Applications, vol. 14, no. 1, pp. 17–30, 2008. 7 J. Jaro ˇ s and T. Kusano, “Self-adjoint differential equations ... Corporation Advances in Difference Equations Volume 2010, Article ID 673761, 16 pages doi:10.1155/2010/673761 Research Article Regularly Varying Solutions of Second- Order Difference Equations with Arbitrary ... Emden-Fowler difference equations, ” Central European Journal of Mathematics , vol. 7, no. 2, pp. 322–334, 2009. 13 P. ˇ Reh ´ ak, “Oscillatory properties of second order half-linear difference equations, ”...

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... Corporation Advances in Difference Equations Volume 2011, Article ID 879649, 14 pages doi:10.1155/2011/879649 Research Article Exponential Stability of Two Coupled Second- Order Evolution Equations Qian Wan and ... be applied to concrete partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution equations one is an integro-differential equation ... using the multiplier technique, we prove that the energy of a system of two coupled second order evolution equations one is an integro-differential equation decays exponentially if the convolution...

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... in the reverse order, ” Applied Mathematics and Computation, vol. 117, no. 1, pp. 1–14, 2001. 8 P. J. Torres and M. Zhang, “A monotone iterative scheme for a nonlinear second order equation ... “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, pp. 643–662, 2003. 10 ... Chu, P. J. Torres, and M. Zhang, “Periodic solutions of second order non-autonomous singular dynamical systems,” Journal of Differential Equations, vol. 239, no. 1, pp. 196–212, 2007. 4 D. Franco...

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... higher- order nonlinear fractional differential equations, ” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009. 14 B. Ahmad and J. R. Graef, “Coupled systems of nonlinear ... 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 ... 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...

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... boundary value problems for nonlinear second- order ordinary differential equations was initiated by Lomtatidze 4, 5. Since then, the nonlinear second- order multipoint boundary value problems ... index theory,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 7, pp. 4319–4332, 2001. 4 A. G. Lomtatidze, “A boundary value problem for second- order nonlinear ordinary differential equations ... Differential Equations, vol. 2002, no. 18, pp. 1–16, 2002. 23 M. Pei and S. K. Chang, “The generalized quasilinearization method for second- order three-point boundary value problems,” Nonlinear...

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... problems for second- order difference equations. Existence of eigenvalues is proved, numbers of their eigenvalues are calculated, and their relationships between the eigenvalues of second- order difference ... Corporation Advances in Difference Equations Volume 2009, Article ID 347291, 18 pages doi:10.1155/2009/347291 Research Article Inequalities among Eigenvalues of Second- Order Difference Equations with General ... γy  b   δy Δ  b   0, 2.9 18 Advances in Difference Equations 4 Y. Wang and Y. Shi, “Eigenvalues of second- order difference equations with periodic and antiperiodic boundary conditions,”...

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... differential equations of second order, ” Annals of Mathematics, vol. 65, pp. 197–202, 1957. 6 R. Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” ... theorem of second- order differential equations see Section 1. Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations ... Annals of Differential Equations, vol. 19, no. 3, pp. 480–486, 2003. 7 R K. Zhuang and H W. Wu, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Applied...

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... Gatica, V. Oliker, and P. Waltman, “Singular nonlinear boundary value problems for second- order ordinary differential equations, ” Journal of Differential Equations, vol. 79, no. 1, pp. 62–78, 1989. 15 ... “Solutions to second- order three-point problems on time scales,” Journal of Difference Equations and Applications, vol. 8, no. 8, pp. 673–688, 2002. 8 D. R. Anderson and I. Y. Karaca, “Higher -order ... Emden-Fowler equations, ” Advances in Difference Equations, vol. 2008, Article ID 796851, 13 pages, 2008. 6 B. Ahmad and J. J . Nieto, “The monotone iterative technique for three-point second- order integrodifferential...

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