Variational approaches to systems of Sturm–Liouville boundary value problems

2020 ◽  
pp. 2150032
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Shahin Moradi
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Technical Approach ◽  
Three Solutions ◽  
Value System ◽  
Sturm Liouville ◽  
Variational Approaches

In this paper, we consider the existence of one solution and three solutions for the boundary value system with Sturm–Liouville boundary conditions [Formula: see text] for [Formula: see text]. Our technical approach is based on variational methods. In addition, examples are provided to illustrate our results.

Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems

1999 ◽  
Vol 6 (5) ◽  
pp. 415-420
Author(s):  
John M. Davis ◽  
Paul W. Eloe ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Three Solutions ◽  
Continuous Growth ◽  
Order Nonlinear Differential Equation ◽  
Triple Positive Solutions

Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.

scholarly journals EXPRESSIONS FOR FUČIK SPECTRA FOR STURM‐LIOUVILLE BVP

2007 ◽  
Vol 12 (1) ◽  
pp. 51-60
Author(s):  
Tatjana Garbuza
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Explicit Formulas ◽  
Sturm Liouville

We provide explicit formulas for the Pučik spectra of boundary value problems with the Sturm‐Liouville boundary conditions.

scholarly journals TRANSFORMATION OF STURM–LIOUVILLE PROBLEMS WITH DECREASING AFFINE BOUNDARY CONDITIONS

2004 ◽  
Vol 47 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Paul A. Binding ◽  
Patrick J. Browne ◽  
Warren J. Code ◽  
Bruce A. Watson
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Subject Classification ◽  
Darboux Transformations ◽  
Sturm Liouville

AbstractWe consider Sturm–Liouville boundary-value problems on the interval $[0,1]$ of the form $-y''+qy=\lambda y$ with boundary conditions $y'(0)\sin\alpha=y(0)\cos\alpha$ and $y'(1)=(a\lambda+b)y(1)$, where $a\lt0$. We show that via multiple Crum–Darboux transformations, this boundary-value problem can be transformed ‘almost’ isospectrally to a boundary-value problem of the same form, but with the boundary condition at $x=1$ replaced by $y'(1)\sin\beta=y(1)\cos\beta$, for some $\beta$.AMS 2000 Mathematics subject classification: Primary 34B07; 47E05; 34L05

scholarly journals Existence principles for second order nonresonant boundary value problems

1994 ◽  
Vol 7 (4) ◽  
pp. 487-507 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Carathéodory Function ◽  
Sturm Liouville

We discuss the two point singular “nonresonant” boundary value problem 1p(py′)′=f(t,y,py′) a.e. on [0,1] with y satisfying Sturm Liouville, Neumann, Periodic or Bohr boundary conditions. Here f is an L1-Carathéodory function and p∈C[0,1]∩C1(0,1) with p>0 on (0,1).

scholarly journals TYPES AND MULTIPLICITY OF SOLUTIONS TO STURM–LIOUVILLE BOUNDARY VALUE PROBLEM

2015 ◽  
Vol 20 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Maria Dobkevich ◽  
Felix Sadyrbaev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Boundary Value Problems ◽  
Multiplicity Of Solutions ◽  
Different Types ◽  
Sturm Liouville

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.

An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
Chinare G. Ibadzadeh ◽  
Ibrahim M. Nabiev
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Spectral Data ◽  
Spectral Parameter ◽  
Boundary Value ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

AbstractIn this paper a boundary value problem is considered generated by the Sturm–Liouville equation and non-separated boundary conditions, one of which contains a spectral parameter. We give a uniqueness theorem, develop an algorithm for solving the inverse problem of reconstruction of boundary value problems with spectral data. We use the spectra of two boundary value problems and some sequence of signs as a spectral data.

Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line

1984 ◽  
Vol 97 ◽  
pp. 259-263 ◽  
Author(s):  
J. F. Toland
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Simple Proof ◽  
Boundary Value ◽  
Half Line ◽  
Linear Boundary ◽  
Autonomous Case ◽  
Sturm Liouville ◽  
Image Position

SynopsisThis note gives a simple proof of uniqueness for positive solutions of certain non-linear boundary value problems on ℝ+ which are typified by the equationwith boundary conditions u′(0) = u(+∞) = 0. In the autonomous case (r ≡ 1), this is easy to see, by quadrature. The proof here supposes r to be non-increasing on ℝ+.

scholarly journals Existence of2m-1Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yanmei Sun ◽  
Zengqin Zhao
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Linear Functional ◽  
Boundary Value ◽  
Half Line ◽  
Multiple Positive Solutions ◽  
Functional Boundary ◽  
Sturm Liouville ◽  
Functional Boundary Conditions

By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

Sign in / Sign up

Export Citation Format

Share Document