Abstract

We consider a nonlinear parametric problem driven by the pp-Laplace differential operator. For all large enough values of the parameter λ\lambda, we show that the problem has a smallest positive solution uλ∗∈C01(Ω‾)u_{\lambda}^*\in C^1_0 (\overline{\Omega}). We examine the monotonicity and continuity properties of the map λ⟼uλ∗\lambda\longmapsto u^*_{\lambda}. Finally we establish the existence of nodal (sign changing) solutions.

Author information

Contact details are reproduced from the original publication and may be historical.

Leszek Gasiński

Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Kraków, Poland

Leszek.Gasinski@ii.uj.edu.pl

Nikolaos S. Papageorgiou

National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

npapg@math.ntua.gr

Keywords

  • Extremal positive solutions
  • nonlinear regularity
  • nonlinear maximum principle
  • nodal solutions
  • p-logistic equation

Mathematics Subject Classification

35J20, 35J65, 35P30

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Suggested citation

L. Gasiński, N. S. Papageorgiou. “Positive, Extremal and Nodal Solutions for Nonlinear Parametric Problems.” Journal of Convex Analysis 24 (2017), No. 1, 261–285. https://doi.org/10.68381/jca24018

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.