On the Number of Solutions for a Certain Class of Nonlinear Second-Order Boundary-Value Problems

2021 ◽  
Author(s):  
A. Kirichuka ◽  
F. Sadyrbaev
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Number Of Solutions

scholarly journals Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance

2007 ◽  
Vol 14 (2) ◽  
pp. 351-360
Author(s):  
Felix Sadyrbaev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Asymptotically Linear ◽  
Number Of Solutions ◽  
Multiplicity Of Solutions ◽  
At Resonance

Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

scholarly journals Boundary value problems for singular second order equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Alessandro Calamai ◽  
Cristina Marcelli ◽  
Francesca Papalini
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Second Order Equations

Well-posedness of boundary value problems for a second-order equation

2009 ◽  
Vol 80 (2) ◽  
pp. 650-652 ◽  
Author(s):  
V. A. Kostin ◽  
M. N. Nebol’sina
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Order Equation ◽  
Second Order ◽  
Well Posedness
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