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Solutions with sign information for nonlinear nonhomogeneous problems
Author(s) -
S. Papageorgiou Nikolaos,
Winkert Patrick
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800083
Subject(s) - mathematics , sign (mathematics) , nonlinear system , parametric statistics , bifurcation , boundary value problem , operator (biology) , mathematical analysis , set (abstract data type) , type (biology) , state (computer science) , algorithm , ecology , biochemistry , statistics , physics , chemistry , repressor , quantum mechanics , biology , computer science , transcription factor , gene , programming language
We consider a parametric elliptic equation driven by a nonlinear nonhomogeneous differential operator and with a Robin boundary condition. In the first part we prove the existence of positive solutions and state a bifurcation‐type result describing how the set of positive solutions changes as the parameter λ > 0 varies. In the second part we show that problem admits nodal (sign‐changing) solutions provided the parameter λ > 0 is sufficiently large.
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