Address.University of Perugia,
Department of Mathematics and Computer Science,
via Vanvitelli 1, Perugia 06123, Italy
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
University of Roma `Tor Vergata',
Department of Mathematics,
via della Ricerca Scientifica, Roma 00133, Italy
E-mail. npapg@math.ntua.gr
Abstract.
In this note we prove the existence of extremal
solutions of the quasilinear Neumann problem $-(|x'(t)|^{p-2}x'(t))'
= f(t, x(t), x'(t))$, a.e. on $T$, $x'(0) =
x'(b) =0$, $2\leq p < \infty$ in the order interval
$[\psi,\varphi]$, where $\psi$ and $\varphi$ are respectively a
lower and an upper solution of the Neumann problem.
AMSclassification. 35J60, 35J65.
Keywords. Upper solution, lower solution, order interval, truncation function, penalty function, pseudomonotone operator, coercive operator, Leray-Schauder principle, maximal solution, minimal solution.