Global Multiplicity of Positive Solutions for Nonlinear Robin Problems with an Indefinite Potential Term

Eylem Öztürk; Nikolaos S. Papageorgiou

doi:10.1007/s00025-024-02142-2

Global Multiplicity of Positive Solutions for Nonlinear Robin Problems with an Indefinite Potential Term

Eylem Öztürk
, Nikolaos S. Papageorgiou

Division of Analysis and Theory of Functions

National Technical University of Athens

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction is parametric and exhibits the competing effects of a concave (sublinear) and of a convex (superlinear) terms (“concave-convex” problem). The parameter multiplies the convex term. We prove an existence and multiplicity theorem which is global in parameter.

Original language	English
Article number	113
Journal	Results in Mathematics
Volume	79
Issue number	3
DOIs	https://doi.org/10.1007/s00025-024-02142-2
Publication status	Published - May 2024

Keywords

35J20
35J60
Nonlinear nonhomogeneous differential operator
indefinite potential
nonlinear regularity
positive solutions
truncations and comparisons

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10.1007/s00025-024-02142-2

Cite this

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abstract = "We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction is parametric and exhibits the competing effects of a concave (sublinear) and of a convex (superlinear) terms (“concave-convex” problem). The parameter multiplies the convex term. We prove an existence and multiplicity theorem which is global in parameter.",

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N2 - We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction is parametric and exhibits the competing effects of a concave (sublinear) and of a convex (superlinear) terms (“concave-convex” problem). The parameter multiplies the convex term. We prove an existence and multiplicity theorem which is global in parameter.

AB - We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction is parametric and exhibits the competing effects of a concave (sublinear) and of a convex (superlinear) terms (“concave-convex” problem). The parameter multiplies the convex term. We prove an existence and multiplicity theorem which is global in parameter.

KW - 35J20

KW - 35J60

KW - Nonlinear nonhomogeneous differential operator

KW - indefinite potential

KW - nonlinear regularity

KW - positive solutions

KW - truncations and comparisons

UR - https://www.scopus.com/pages/publications/85186395841

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DO - 10.1007/s00025-024-02142-2

M3 - Article

AN - SCOPUS:85186395841

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VL - 79

JO - Results in Mathematics

JF - Results in Mathematics

IS - 3

M1 - 113

ER -

Global Multiplicity of Positive Solutions for Nonlinear Robin Problems with an Indefinite Potential Term

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Keywords

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