Multiplicity results for systems of asymptotically linear second order equations

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Anna Capietto ◽  
Francesca Dalbono
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Asymptotically Linear ◽  
Multiplicity Results ◽  
Number Of Zeros ◽  
Existence And Multiplicity ◽  
Abstract Continuation Theorem ◽  
Nodal Properties ◽  
Second Order Equations

AbstractWe prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

scholarly journals Multiplicity results for asymmetric boundary value problems with indefinite weights

2004 ◽  
Vol 2004 (11) ◽  
pp. 957-979
Author(s):  
Francesca Dalbono
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Asymptotically Linear ◽  
Topological Methods ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Rotation Numbers ◽  
Indefinite Weights ◽  
Nodal Properties

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.

scholarly journals Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
A. Gritsans ◽  
F. Sadyrbaev ◽  
I. Yermachenko
Keyword(s):  
Vector Field ◽  
Dirichlet Boundary ◽  
Second Order ◽  
Dirichlet Boundary Conditions ◽  
Order System ◽  
Dirichlet Boundary Value Problem ◽  
Asymptotically Linear ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Field Rotation

We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.

ChemInform Abstract: A STUDY OF THE UPPER AND LOWER BOUNDS OF THE SECOND-ORDER PERTURBATION ENERGY

1974 ◽  
Vol 5 (40) ◽  
pp. no-no
Author(s):  
TOKIO YAMABE ◽  
KAZUYOSHI TANAKA ◽  
SHINGO ISHIMARU ◽  
KENICHI FUKUI
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Order Perturbation ◽  
Upper And Lower Bounds ◽  
Perturbation Energy

On the Zeros of Power Series with Exponential Logarithmic Coefficients

1981 ◽  
Vol 24 (3) ◽  
pp. 257-271 ◽  
Author(s):  
W. Gawronski ◽  
U. Stadtmüller
Keyword(s):  
Power Series ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Number Of Zeros ◽  
Logarithmic Coefficients ◽  
Image Position

In this paper we investigate the zeros of power series1for some functions of coefficients A. In particular, we derive upper and lower bounds for the number of zeros of f in its domain of analyticity.

A Landesman–Lazer-type condition for asymptotically linear second-order equations with a singularity

2012 ◽  
Vol 142 (6) ◽  
pp. 1263-1277 ◽  
Author(s):  
Alessandro Fonda ◽  
Maurizio Garrione
Keyword(s):  
Periodic Problem ◽  
Second Order ◽  
Type Condition ◽  
Asymptotically Linear ◽  
Existence Of A Solution ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Linear Behaviour ◽  
Image Position ◽  
Second Order Equations

We consider the T-periodic problemwhere g: [0,T]×]0,+∞[→ℝ exhibits a singularity of a repulsive type at the origin, and an asymptotically linear behaviour at infinity. In particular, for large x, g(t, x) is controlled from both sides by two consecutive asymptotes of the T-periodic Fučik spectrum, with possible equality on one side. Using a suitable Landesman–Lazer-type condition, we prove the existence of a solution.

scholarly journals Multiplicity and Bifurcation of Solutions for a Class of Asymptotically Linear Elliptic Problems on the Unit Ball

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Benlong Xu
Keyword(s):  
Unit Ball ◽  
Linear Function ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Global Bifurcation ◽  
Asymptotically Linear ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Bifurcation Of Solutions

This paper mainly dealt with the exact number and global bifurcation of positive solutions for a class of semilinear elliptic equations with asymptotically linear function on a unit ball. As byproducts, some existence and multiplicity results are also obtained on a general bounded domain.

Sign in / Sign up

Export Citation Format

Share Document