Geodesic
The Neumann problem for quasilinear differential equations
Archivum mathematicum, Tome 40 (2004) no. 4, pp. 321-333

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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.
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.
Classification : 34B15, 35J25, 35J60, 35J65
Keywords: upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; Leray-Schauder principle; maximal solution; minimal solution 
Cardinali, Tiziana; Papageorgiou, Nikolaos S.; Servadei, Raffaella. The Neumann problem for quasilinear differential equations. Archivum mathematicum, Tome 40 (2004) no. 4, pp. 321-333. http://geodesic.mathdoc.fr/item/ARM_2004_40_4_a0/
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     title = {The {Neumann} problem for quasilinear differential equations},
     journal = {Archivum mathematicum},
     pages = {321--333},
     year = {2004},
     volume = {40},
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     mrnumber = {2129954},
     zbl = {1122.35030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004_40_4_a0/}
}
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