On the Existence of Infinite Sequences of Ordered Positive Solutions of Nonlinear Elliptic Eigenvalue Problems

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Francisco Júlio S. A. Corrêa ◽  
Marcos L. M. Carvalho ◽  
José Valdo A. Gonçalves ◽  
Kaye O. Silva
Keyword(s):  
Positive Solutions ◽  
Topological Degree ◽  
Eigenvalue Problems ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems ◽  
Infinite Sequences

AbstractIn this work, we employ minimization arguments and topological degree theory for mappings of type

scholarly journals Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper is concerned with the existence of positive solutions for a class of boundary value problems of fractional differential equations with parameter. The main tools used here are bifurcation techniques and topological degree theory. Finally, an example is worked out to demonstrate the main result.

scholarly journals Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian

2018 ◽  
Vol 20 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Alexander Quaas ◽  
Aliang Xia
Keyword(s):  
Positive Solutions ◽  
Fractional Laplacian ◽  
Degree Theory ◽  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic Problem ◽  
Topological Degree Theory ◽  
Scaling Method ◽  
Smooth Bounded Domain ◽  
Nonlinear Elliptic

In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: [Formula: see text] where [Formula: see text] denotes the fractional Laplacian and [Formula: see text] is a smooth bounded domain in [Formula: see text]. It shown that under some assumptions on [Formula: see text] and [Formula: see text], the problem has at least one positive solution [Formula: see text]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.

scholarly journals Positive Solutions of Nonlinear Elliptic Equations with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hua Luo
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Eigenvalue Problems ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Elliptic Eigenvalue Problems ◽  
Bifurcation From Interval

This paper discusses bifurcation from interval for the elliptic eigenvalue problems with nonlinear boundary conditions and studies the behavior of the bifurcation components.

Existence results for nonlinear periodic boundary-value problems

2009 ◽  
Vol 52 (1) ◽  
pp. 79-95 ◽  
Author(s):  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Topological Degree ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Finite Interval ◽  
Nonlinear Differential Equations ◽  
Degree Theory ◽  
Periodic Boundary Conditions ◽  
Existence Results ◽  
Topological Degree Theory ◽  
Periodic Boundary Value Problems

AbstractWe study a class of second-order nonlinear differential equations on a finite interval with periodic boundary conditions. The nonlinearity in the equations can take negative values and may be unbounded from below. Criteria are established for the existence of non-trivial solutions, positive solutions and negative solutions of the problems under consideration. Applications of our results to related eigenvalue problems are also discussed. Examples are included to illustrate some of the results. Our analysis relies mainly on topological degree theory.

scholarly journals Bifurcation of Positive Solutions for a Class of Boundary Value Problems of Fractional Differential Inclusions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yansheng Liu ◽  
Huimin Yu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Topological Degree ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Degree Theory ◽  
Fractional Differential Inclusions ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

Using Krein-Rutman theorem, topological degree theory, and bifurcation techniques, this paper investigates the existence of positive solutions for a class of boundary value problems of fractional differential inclusions.

scholarly journals Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional p , q -Difference Equations under p , q -Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yongyang Liu ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Topological Degree Theory ◽  
Integral Boundary

This paper is mainly concerned with a class of fractional p , q -difference equations under p , q -integral boundary conditions. Multiple positive solutions are established by using the topological degree theory and Krein–Rutman theorem. Finally, two examples are worked out to illustrate the main results.

Sign in / Sign up

Export Citation Format

Share Document