Geodesic
A Multivalued Nonlinear System with the Vector p-Laplacian on the Semi-Infinity Interval
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 217-228

Voir la notice de l'article provenant de la source Cambridge University Press

We study a second order nonlinear system driven by the vector $p$ -Laplacian, with a multivalued nonlinearity and defined on the positive time semi-axis ${{\mathbb{R}}_{+}}.$ Using degree theoretic techniques we solve an auxiliary mixed boundary value problem defined on the finite interval $\left[ 0,\,n \right]$ and then via a diagonalization method we produce a solution for the original infinite time horizon system.
DOI : 10.4153/CMB-2008-023-8
Mots-clés : 34A60, semi-infinity interval, vector, p-Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map 
Filippakis, Michael E.; Papageorgiou, Nikolaos S. A Multivalued Nonlinear System with the Vector p-Laplacian on the Semi-Infinity Interval. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 217-228. doi: 10.4153/CMB-2008-023-8
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[1] [1] Agarwal, R. and O’Regan, D., Boundary value problems of nonsingular type on the semi-infinity interval. Tohoku Math. J. 51(1999), no. 3, 391–397. Google Scholar

[2] [2] Bader, R., A topological fixed point index theory for evolution inclusions. Z. Anal. Anwendungen 20(2001), no. 1, 3–15. Google Scholar

[3] [3] Constantin, A., On an infinite interval boundary value problem. Ann. Mat. Pura Appl. 176(1999), 379–394. Google Scholar

[4] [4] Denkowski, Z., Migórski, S., and Papageorgiou, N. S., An Introduction to Nonlinear Analysis: Theory. Kluwer Academic, Boston, 2003. Google Scholar

[5] [5] Denkowski, Z., Migórski, S., and Papageorgiou, N. S., An Introduction to Nonlinear Analysis:. Applications. Kluwer Academic, Boston, 2003. Google Scholar

[6] [6] Gasinski, L. and Papageorgiou, N. S., Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems. Series in Mathematical Analysis and Applications 8. Chapman and Hall/CRC Press, Boca Raton, FL, 2005. Google Scholar

[7] [7] Granas, A., Guenther, R., Lee, J., and O’Regan, D., Boundary value problems on infinite intervals and semiconductor devices. J. Math. Anal. Appl. 116(1986), no. 2, 335–348. Google Scholar

[8] [8] Hartman, P., Ordinary Differential Equations. Wiley, New York, 1964. Google Scholar

[9] [9] Hu, S. and Papageorgiou, N. S., Handbook of Multivalued Analysis. I: Theory. Mathematics and Its Applications 419, Kluwer, Dordrecht, 1997. Google Scholar

[10] [10] Ma, R., Existence of positive solutions for second-order boundary value problems on infinite intervals. Appl. Math. Letters, 16(2003), no. 1, 33–39. Google Scholar

[11] [11] Nagumo, M., Über das Randwertproblem der nicht linearen gewöhnlichen Differentialgleichungen zweiter Ordnung. Proc. Phys.-Math. Soc. Japan 24(1942), 845–851. Google Scholar

[12] [12] O’Regan, D., A note on Leray-Schauder alternatives for the decomposable maps of Bader. Nonlinear Anal., to appear. Google Scholar

[13] [13] Wintner, A., The nonlocal existence problem of ordinary differential equations. Amer. J. Math. 67(1945), 277–284. Google Scholar

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