Positive solutions for (p, 2)-equations with superlinear reaction and a concave boundary term

Papageorgiou, Nikolaos S. and Scapellato, Andrea: Positive solutions for (p, 2)-equations with superlinear reaction and a concave boundary term. In: Electronic journal of qualitative theory of differential equations 4. pp. 1-19. (2020)

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Abstract

We consider a nonlinear boundary value problem driven by the (p, 2)- Laplacian, with a (p − 1)-superlinear reaction and a parametric concave boundary term (a “concave-convex” problem). Using variational tools (critical point theory) together with truncation and comparison techniques, we prove a bifurcation type theorem describing the changes in the set of positive solutions as the parameter λ > 0 varies. We also show that for every admissible parameter λ > 0, the problem has a minimal positive solution uλ and determine the monotonicity and continuity properties of the map λ 7→ uλ.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2020
Number: 4
ISSN: 1417-3875
Page Range: pp. 1-19
DOI: https://doi.org/10.14232/ejqtde.2020.1.4
Uncontrolled Keywords: Pozitív megoldás, Differenciaegyenlet
Additional Information: Bibliogr.: p. 18-19. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 28. 09:55
Last Modified: 2020. Jan. 28. 09:55
URI: http://acta.bibl.u-szeged.hu/id/eprint/66370

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