The Neumann problem for quasilinear differential equations

Cardinali, Tiziana ; Papageorgiou, Nikolaos S. ; Servadei, Raffaella

Archivum Mathematicum, Tome 040 (2004), p. 321-333 / Harvested from Czech Digital Mathematics Library

Résumé

In this note we prove the existence of extremal solutions of the quasilinear Neumann problem $-( \vert x^{^{\prime }}(t) \vert ^{p-2}x^{^{\prime }}(t))^{^{\prime }} = f(t,x(t),x ^{^{\prime }}(t))$, a.e. on $T$, $x^{^{\prime }}(0) = x^{^{\prime }}(b) =0$, $2\le p < \infty $ in the order interval $[\psi ,\varphi ]$, where $\psi $ and $\varphi $ are respectively a lower and an upper solution of the Neumann problem.

Détail

Publié le : 2004-01-01

MR 2129954 | Zbl 1122.35030

Classification:  34B15,  35J25,  35J60,  35J65

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