scholarly journals Applications of maximum modulus method and Phragmén–Lindelöf method for second-order boundary value problems with respect to the Schrödinger operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zhen Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Schrödinger Operator ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Schrodinger Operator ◽  
Uniqueness Of The Solution ◽  
Modulus Method

Abstract In this paper, we present a reliable combination of the maximum modulus method with respect to the Schrödinger operator (Meng in J. Syst. Sci. Complex. 16:446–452, 2003) and Phragmén–Lindelöf method (Shehu in Matematiche 64:57–66, 2015) to investigate the solution of a second-order boundary value problem with respect to the Schrödinger operator. We establish the uniqueness of the solution for this problem. The results reveal that this method is effective and simple.

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.

Existence of Two Solutions for a Second-Order Discrete Boundary Value Problem

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Pasquale Candito ◽  
Giovanni Molica Bisci
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Discrete Boundary Value Problem

AbstractThe existence of two nontrivial solutions for a class of nonlinear second-order discrete boundary value problems is established. The approach adopted is based on variational methods.

ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

2001 ◽  
Vol 6 (1) ◽  
pp. 147-155 ◽  
Author(s):  
S. Rutkauskas
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Second Order ◽  
Type Problem ◽  
Dirichlet Type ◽  
Holder Class ◽  
Uniqueness Of The Solution ◽  
Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

scholarly journals Solvability of singular second order m-point boundary value problems of Dirichlet type

2005 ◽  
Vol 71 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Ruyun Ma ◽  
Bevan Thompson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Continuation Theorem ◽  
Point Boundary ◽  
Dirichlet Type ◽  
Carathéodory Conditions

Let f: [0, 1] × ℝ2 → ℝ be a function satisfying the Carathéodory conditions and t (1 − t) e (t) ∈ L1(0, 1). Let ai ∈ ℝ and ξi ∈ (0, 1) for i = 1, …, m − 2 where 0 < ξ1 < ξ2 < … < ξm−2 < 1. In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem The proof of our main result is based on the Leray-Schauder continuation theorem.

scholarly journals Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

Matrix boundary-value problems for differential equations with p-Laplacian

2020 ◽  
Vol 17 (1) ◽  
pp. 41-57
Author(s):  
Olga Nesmelova
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Arbitrary Function ◽  
Algebraic System ◽  
Boundary Value ◽  
System Of Differential Equations ◽  
Differential Algebraic System ◽  
Uniqueness Of The Solution

We consider the boundary-value problem for a linear system of differential equations with matrix p-Laplacian, which is reduced to the traditional differential-algebraic system with an unknown in the form of the vector function. A generalization of various boundary-value problems for differential equations with p-Laplacian, which preserves the features of the solution of such problems, namely, the lack of uniqueness of the solution and, in this case, the dependence of the desired solution on an arbitrary function, is given.

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