Existence and multiplicity results for nonlinear nonautonomous second-order systems

2008 ◽  
Vol 68 (6) ◽  
pp. 1611-1626 ◽  
Author(s):  
Michael E. Filippakis
Keyword(s):  
Second Order ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Second Order Systems

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 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.

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