scholarly journals Nodal Solutions for Neumann Problems with a Nonhomogeneous Differential Operator

2013 ◽  
Vol 56 (1) ◽  
pp. 63-79 ◽  
Author(s):  
Michael E. Filippakis ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Nodal Solutions ◽  
Neumann Problems ◽  
Nonhomogeneous Differential Operator

Coercive and noncoercive nonlinear Neumann problems with indefinite potential

2016 ◽  
Vol 28 (3) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Differential Operator ◽  
Neumann Problems ◽  
Nonhomogeneous Differential Operator ◽  
Indefinite Potential ◽  
Nonlinear Neumann Problems

AbstractWe consider nonlinear Neumann problems driven by a nonhomogeneous differential operator and an indefinite potential. In this paper we are concerned with two distinct cases. We first consider the case where the reaction is (

Arbitrarily small nodal solutions for nonhomogeneous Robin problems

2021 ◽  
pp. 1-15
Author(s):  
Shengda Zeng ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Robin Problem ◽  
Nodal Solutions ◽  
Nonhomogeneous Differential Operator ◽  
Variational Tools

In the present paper, we consider a nonlinear Robin problem driven by a nonhomogeneous differential operator and with a reaction which is only locally defined. Using cut-off techniques and variational tools, we show that the problem has a sequence of nodal solutions converging to zero in C 1 ( Ω ‾ ).

A Multiplicity Theorem for p-Superlinear Neumann Problems with a Nonhomogeneous Differential Operator

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Giuseppina Barletta ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Critical Point Theory ◽  
Point Theory ◽  
Smooth Solutions ◽  
Neumann Problems ◽  
Nonhomogeneous Differential Operator ◽  
Nonlinear Neumann Problem ◽  
Multiplicity Theorem ◽  
Truncation Techniques ◽  
Special Case

AbstractWe consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator (special case is the p-Laplacian) with a (p − 1)-superlinear Carathéodory reaction term, which need not satisfy the usual in such cases Ambrosetti-Rabinowitz condition. Using variational methods based on the critical point theory coupled with suitable truncation techniques, we show that the problem has at least five nontrivial smooth solutions.

Infinitely Many Nodal Solutions for Nonlinear Nonhomogeneous Robin Problems

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Differential Operator ◽  
Robin Problem ◽  
Nodal Solutions ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear Robin problem driven by a nonhomogeneous differential operator which incorporates the

scholarly journals CONSTANT SIGN AND NODAL SOLUTIONS FOR NONLINEAR ROBIN EQUATIONS WITH LOCALLY DEFINED SOURCE TERM

2020 ◽  
Vol 25 (3) ◽  
pp. 374-390
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Differential Operator ◽  
Source Term ◽  
Constant Sign ◽  
Robin Problem ◽  
Smooth Solutions ◽  
Nodal Solutions ◽  
Nonhomogeneous Differential Operator ◽  
Special Cases ◽  
Variational Tools ◽  
Nonlinear Nonhomogeneous Differential Operator

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

Positive Solutions for the Generalized Nonlinear Logistic Equations

2016 ◽  
Vol 59 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Type Result ◽  
Logistic Equations ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiòusive type. Using variationalmethods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

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