Global bifurcation diagrams of positive solutions for a class of 1-D superlinear indefinite problems

05/19/2020
by   Martin Fencl, et al.
0

This paper analyzes the structure of the set of positive solutions of a class of one-dimensional symmetric superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast point-wise decay of the positive solutions as λ↓ -∞ in the region where a(x)<0, and solve positively the conjecture of R. Gómez-Reñasco and J. López-Gómez in two special cases of interest, where we show the existence of 2^n+1-1 positive solutions for sufficiently negative λ. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/20/2020

Nodal solutions of weighted indefinite problems

This paper analyzes the structure of the set of nodal solutions of a cla...
12/06/2020

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study

We consider the generalized Benjamin-Ono (gBO) equation on the real line...
01/21/2021

Differential Euler: Designing a Neural Network approximator to solve the Chaotic Three Body Problem

The three body problem is a special case of the n body problem where one...
12/30/2020

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

We present a detailed numerical study of solutions to the Zakharov-Kuzne...
05/27/2020

Oligopoly Dynamics

The present notes summarise the oligopoly dynamics lectures professor Lu...
08/15/2019

On boundedness and growth of unsteady solutions under the double porosity/permeability model

There is a recent surge in research activities on modeling the flow of f...
11/12/2019

Existence and nonexistence results of radial solutions to singular BVPs arising in epitaxial growth theory

The existence and nonexistence of stationary radial solutions to the ell...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.