Geodesic
Positive, Extremal and Nodal Solutions for Nonlinear Parametric Problems
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 261-285
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We consider a nonlinear parametric problem driven by the $p$-Laplace differential operator. For all large enough values of the parameter $\lambda$, we show that the problem has a smallest positive solution $u_{\lambda}^*\in C^1_0 (\overline{\Omega})$. We examine the monotonicity and continuity properties of the map $\lambda\longmapsto u^*_{\lambda}$. Finally we establish the existence of nodal (sign changing) solutions.
Classification : 35J20, 35J65, 35P30
Mots-clés : Extremal positive solutions, nonlinear regularity, nonlinear maximum principle, nodal solutions, p-logistic equation 
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     author = {L. Gasinski and N. S. Papageorgiou},
     title = {Positive, {Extremal} and {Nodal} {Solutions} for {Nonlinear} {Parametric} {Problems}},
     journal = {Journal of convex analysis},
     pages = {261--285},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a17/}
}
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L. Gasinski; N. S. Papageorgiou. Positive, Extremal and Nodal Solutions for Nonlinear Parametric Problems. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 261-285. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a17/