scholarly journals On a $(p,q)$-Laplacian problem with parametric concave term and asymmetric perturbation

2018 ◽  
Vol 29 (1) ◽  
pp. 109-125 ◽  
Author(s):  
Salvatore Marano ◽  
Sunra Mosconi ◽  
Nikolaos Papageorgiou
Keyword(s):  
Asymmetric Perturbation ◽  
Concave Term

Nonlinear Parametric Robin Problems with Combined Nonlinearities

2015 ◽  
Vol 15 (3) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Growth Condition ◽  
Morse Theory ◽  
Constant Sign ◽  
Robin Problem ◽  
Three Solutions ◽  
Multiplicity Theorem ◽  
Solutions Of Constant Sign ◽  
Semilinear Problem ◽  
Concave Term

AbstractWe consider a nonlinear parametric Robin problem driven by the p-Laplacian. We assume that the reaction exhibits a concave term near the origin. First we prove a multiplicity theorem producing three solutions with sign information (positive, negative and nodal) without imposing any growth condition near ±∞ on the reaction. Then, for problems with subcritical reaction, we produce two more solutions of constant sign, for a total of five solutions. For the semilinear problem (that is, for p = 2), we generate a sixth solution but without any sign information. Our approach is variational, coupled with truncation, perturbation and comparison techniques and with Morse theory.

Nodal Solutions for Nonlinear Non-Homogeneous Robin Problems with an Indefinite Potential

2018 ◽  
Vol 61 (4) ◽  
pp. 943-959 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Reaction Function ◽  
Robin Problem ◽  
Nodal Solutions ◽  
Potential Term ◽  
Symmetric Mountain Pass Theorem ◽  
Indefinite Potential ◽  
Concave Term

AbstractWe consider a nonlinear Robin problem driven by a non-homogeneous differential operator plus an indefinite potential term. The reaction function is Carathéodory with arbitrary growth near±∞. We assume that it is odd and exhibits a concave term near zero. Using a variant of the symmetric mountain pass theorem, we establish the existence of a sequence of distinct nodal solutions which converge to zero.

scholarly journals Fredkin and Toffoli Gates Implemented in Oregonator Model of Belousov–Zhabotinsky Medium

2017 ◽  
Vol 27 (03) ◽  
pp. 1750041 ◽  
Author(s):  
Andrew Adamatzky
Keyword(s):  
Thin Layer ◽  
Logical Truth ◽  
Toffoli Gate ◽  
Computing Device ◽  
Excitation Wave ◽  
Dissipative Solitons ◽  
Fredkin Gate ◽  
Image Processors ◽  
Asymmetric Perturbation ◽  
Oregonator Model

A thin-layer Belousov–Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates — Fredkin gate and Toffoli gate — in a BZ medium network of excitable channels with subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates’ design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment — logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

scholarly journals Binary Source Microlensing Event OGLE-2016-BLG-0733: Interpretation of a Long-term Asymmetric Perturbation

2017 ◽  
Vol 153 (3) ◽  
pp. 129 ◽  
Author(s):  
Y. K. Jung ◽  
A. Udalski ◽  
J. C. Yee ◽  
T. Sumi ◽  
A. Gould ◽  
...  
Keyword(s):  
Asymmetric Perturbation

scholarly journals Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-36 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Smooth Solutions ◽  
Dirichlet Problems ◽  
Unbounded Potential ◽  
Indefinite Potential ◽  
Truncation Techniques ◽  
Concave Term

We consider a parametric semilinear Dirichlet problem with an unbounded and indefinite potential. In the reaction we have the competing effects of a sublinear (concave) term and of a superlinear (convex) term. Using variational methods coupled with suitable truncation techniques, we prove two multiplicity theorems for small values of the parameter. Both theorems produce five nontrivial smooth solutions, and in the second theorem we provide precise sign information for all the solutions.

scholarly journals On the set of positive solutions for resonant Robin (p, q)-equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1132-1153
Author(s):  
Nikolaos S. Papageorgiou ◽  
Youpei Zhang
Keyword(s):  
Positive Solutions ◽  
Type Theorem ◽  
Robin Problem ◽  
Continuity Properties ◽  
Concave Term

Abstract We consider a nonlinear Robin problem driven by the (p, q)-Laplacian and a parametric reaction exhibiting the competition of a concave term and of a resonant perturbation. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on ℝ̊+ = (0, +∞). Also, we determine the continuity properties of the solution multifunction.

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