Existence of nontrivial solutions for a nonlinear Sturm–Liouville problem with integral boundary conditions

2008 ◽  
Vol 68 (1) ◽  
pp. 216-225 ◽  
Author(s):  
Zhilin Yang
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Liouville Problem ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
Sturm Liouville

scholarly journals Investigation of the spectrum for the Sturm–Liouville problem with one integral boundary condition

2010 ◽  
Vol 15 (4) ◽  
pp. 501-512 ◽  
Author(s):  
A. Skučaitė ◽  
K. Skučaitė-Bingelė ◽  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Liouville Problem ◽  
Characteristic Functions ◽  
Integral Boundary ◽  
Sturm Liouville ◽  
Nonlocal Integral Boundary Conditions ◽  
Type Boundary ◽  
Type Boundary Condition

In this paper, the Sturm–Liouville problem with one classical first type boundary condition and other nonlocal integral boundary conditions of two cases is investigated. We analyze how complex eigenvalues of these problems depend on the parameters of nonlocal integral boundary conditions. Some new results are given on complex spectra of these problems. Many results are presented as graphs of complex characteristic functions.

scholarly journals STURM-LIOUVILLE PROBLEM FOR STATIONARY DIFFERENTIAL OPERATOR WITH NONLOCAL INTEGRAL BOUNDARY CONDITION

2005 ◽  
Vol 10 (4) ◽  
pp. 377-392 ◽  
Author(s):  
S. Pečiulyte ◽  
O. Štikoniene
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Liouville Problem ◽  
Complex Case ◽  
Integral Boundary ◽  
Sturm Liouville ◽  
Nonlocal Integral Boundary Conditions

The Sturm‐Liouville problem with various types of nonlocal integral boundary conditions is considered in this paper. In the first part of paper we investigate Sturm‐Liouville problem with two cases of nonlocal integral boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such problem in the complex case. In the second part we investigate real eigenvalues case. The spectrum depends of these problems on boundary condition parameters is analyzed. Qualitative behaviour of all eigenvalues subject to nonlocal boundary condition parameters is described. Šiame straipsnyje nagrinejamas Šturmo‐Liuvilio uždavinys su viena nelokaliaja integralinio tipo kraštine salyga. Pirmoje straipsnio dalyje tiriamas Šturmo‐Liuvilio uždavinys su dvieju tipu integraline nelokaliaja salyga. Irodytos tikriniu funkciju ir tikriniu reikšmiu bendrosios savybes komplesineje plokštumoje. Antroje dalyje plačiau ištirtas realiuju tikriniu reikšmiu atvejis. Straipsnyje nagrinejama kaip Šturmo‐Liuvilio uždavinio spektras priklauso nuo kraštiniu salygu parametru. Priklausomai nuo nelokaliuju kraštiniu salygu parametru, aprašytas kokybinis tikriniu reikšmiu pasiskirstymas.

scholarly journals Nontrivial Solutions for a System of Fractional q-Difference Equations Involving q-Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 828 ◽  
Author(s):  
Yaohong Li ◽  
Jie Liu ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Integral Boundary Conditions ◽  
Integral Operators ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
The First Eigenvalue ◽  
Linear Integral ◽  
Linear Integral Operators

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.

scholarly journals Relations between Spectrum Curves of Discrete Sturm-Liouville Problem with Nonlocal Boundary Conditions and Graph Theory. II

2021 ◽  
Vol 62 ◽  
pp. 1-8
Author(s):  
Jonas Vitkauskas ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Graph Theory ◽  
Boundary Conditions ◽  
Critical Points ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Sturm Liouville

In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary conditions.

scholarly journals A second order differential equation with generalized Sturm-Liouville integral boundary conditions at resonance

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1437-1444 ◽  
Author(s):  
Zengji Du ◽  
Jian Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Second Order ◽  
Integral Boundary ◽  
At Resonance ◽  
Sturm Liouville

By using Mawhin coincidence degree theory, we investigate the existence of solutions for a class of second order nonlinear differential equations with generalized Sturm-Liouville integral boundary conditions at resonance. The results extend some known conclusions of integral boundary value problem at resonance for nonlinear differential equations

Sign in / Sign up

Export Citation Format

Share Document