scholarly journals Existence and multiplicity results for second-order discontinuous problems via non-ordered lower and upper solutions

2020 ◽  
Vol 25 (2) ◽  
pp. 617-633
Author(s):  
Rubén Figueroa ◽  
◽  
Rodrigo López Pouso ◽  
Jorge Rodríguez–López
Keyword(s):  
Second Order ◽  
Lower And Upper Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Discontinuous Problems

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.

PERIODIC SOLUTIONS FOR SINGULAR PERTURBATIONS OF THE SINGULAR ϕ-LAPLACIAN OPERATOR

2013 ◽  
Vol 15 (04) ◽  
pp. 1250063 ◽  
Author(s):  
CRISTIAN BEREANU ◽  
DANA GHEORGHE ◽  
MANUEL ZAMORA
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Elasticity ◽  
Singular Perturbations ◽  
Continuous Functions ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Periodic Problems ◽  
Singular Nonlinearities

In this paper, using Leray–Schauder degree arguments and the method of lower and upper solutions, we give existence and multiplicity results for periodic problems with singular nonlinearities of the type [Formula: see text] where r, n, e : [0, T] → ℝ are continuous functions and λ > 0. We also consider some singular nonlinearities arising in nonlinear elasticity or of Rayleigh–Plesset type.

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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