Geodesic
Asymptotic integration of differential equations with singular $p$-Laplacian
Archivum mathematicum, Tome 52 (2016) no. 1, pp. 13-19 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with $p-$Laplacian, where $1 p 2$. We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as $t \rightarrow \infty $.
In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with $p-$Laplacian, where $1 p 2$. We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as $t \rightarrow \infty $.
DOI : 10.5817/AM2016-1-13
Classification : 34D05, 35B40
Keywords: $p$-Laplacian; differential equation; asymptotic integration 
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Medveď, Milan; Pekárková, Eva. Asymptotic integration of differential equations with singular $p$-Laplacian. Archivum mathematicum, Tome 52 (2016) no. 1, pp. 13-19. doi: 10.5817/AM2016-1-13

[1] Agarwal, R.P., Djebali, S., Moussaoui, T., Mustafa, O.G.: On the asymptotic integration of nonlinear differential equations. J. Comput. Appl. Math 202 (2007), 352–376. | DOI | MR | Zbl

[2] Bartušek, M., Medveď, M.: Existence of global solutions for systems of second-order functional-differential equations with $p$-Laplacian. EJDE 40 (2008), 1–8. | MR | Zbl

[3] Bartušek, M., Pekárková, E.: On the existence of proper solutions of quasilinear second order differential equations. EJQTDE 1 (2007), 1–14. | MR

[4] Bihari, I.: A generalization of a lemma of Bellman and its applications to uniqueness problems of differential equations. Acta Math. Hungar. 7 (1956), 81–94. | DOI | MR

[5] Caligo, D.: Comportamento asintotico degli integrali dell’equazione $y^{\prime \prime }(x)+A(x)y(x)=0,$ nell’ipotesi $\lim _{x\rightarrow +\infty }A(x)=0$. Boll. Un. Mat. Ital. (2) 3 (1941), 286–295. | MR

[6] Cohen, D.S.: The asymptotic behavior of a class of nonlinear differntial equations. Proc. Amer. Math. Soc. 18 (1967), 607–609. | DOI | MR

[7] Constantin, A.: On the asymptotic behavior of second order nonlinear differential equations. Rend. Mat. Appl. (7) 13 (4) (1993), 627–634. | MR

[8] Constantin, A.: Solutions globales d’équations différentielles perturbées. C. R. Acad. Sci. Paris Sér. I Math. 320 (11) (1995), 1319–1322. | MR

[9] Constantin, A.: On the existence of positive solutions of second order differential equations. Ann. Mat. Pura Appl. (4) 184 (2) (2005), 131–138. | DOI | MR | Zbl

[10] Dannan, F.M.: Integral inequalities of Gronwall-Bellman-Bihari type and asymptotic behavior of certain second order nonlinear differential equations. J. Math. anal. Appl. 108 (1) (1985), 151–164. | DOI | MR

[11] Kusano, T., Trench, W.F.: Existence of global solutions with prescribed asymptotic behavior for nonlinear ordinary differential equations. J. London Math. Soc.(2) 31 (3) (1985), 478–486. | DOI | MR

[12] Kusano, T., Trench, W.F.: Existence of global solutions with prescribed asymptotic behavior for nonlinear ordinary differential equations. Ann. Mat. Pura Appl. (4) 142 (1985), 381–392. | MR

[13] Lipovan, O.: On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations. Glasgow Math. J. 45 (1) (2003), 179–187. | DOI | MR | Zbl

[14] Medveď, M., Moussaoui, T.: Asymptotic integration of nonlinear $\Phi -$Laplacian differential equations. Nonlinear Anal. 72 (2010), 1–8. | DOI | MR | Zbl

[15] Medveď, M., Pekárková, E.: Existence of global solutions for systems of second-order differential equations with $p$-Laplacian. EJDE 2007 (136) (2007), 1–9. | MR | Zbl

[16] Medveď, M., Pekárková, E.: Long time behavior of second order differential equations with $p$-Laplacian. EJDE 2008 (108) (2008), 1–12. | MR

[17] Mustafa, O.G., Rogovchenko, Y.V.: Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations. Nonlinear Anal. 51 (2002), 339–368. | DOI | MR | Zbl

[18] Mustafa, O.G., Rogovchenko, Y.V.: Asymptotic behavior of nonoscillatory solutions of second-order nonlinear differential equations. Dynamic Systems and Applications 4 (2004), 312–319. | MR | Zbl

[19] Pekárková, E.: Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian. Arch. Math.( Brno) 46 (2010), 135–144. | MR | Zbl

[20] Philos, Ch.G., Purnaras, I.K., Tsamatos, P.Ch.: Large time asymptotic to polynomials solutions for nonlinear differential equations. Nonlinear Anal. 59 (2004), 1157–1179. | DOI | MR

[21] Rogovchenko, S.P., Rogovchenko, Y.V.: Asymptotics of solutions for a class of second order nonlinear differential equations. Portugal. Math. 57 (1) (2000), 17–32.

[22] Rogovchenko, Y.V.: On asymptotic behavior of solutions for a class of second order nonlinear differential equations. Collect. Math. 49 (1) (1998), 113–120. | MR

[23] Tong, J.: The asymptotic behavior of a class of nonlinear differential equations of second order. Proc. Amer. Math. Soc. 54 (1982), 235–236. | DOI | MR | Zbl

[24] Trench, W.F.: On the asymptotic behavior of solutions of second order linear differential equations. Proc. Amer. Math. Soc. 54 (1963), 12–14. | DOI | MR

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