scholarly journals On a boundary value problem for differential equation with p-Laplacian

2011 ◽  
Vol 48 (1) ◽  
pp. 189-195
Author(s):  
Boris Rudolf
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Nonlocal Boundary Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Lower And Upper Solutions ◽  
Existence Of A Solution

Abstract The existence of a solution of a boundary value problem for differential equation with p-Laplacian is proved by the technique of lower and upper solutions. A nonlocal boundary condition and a derivative dependent nonlinearity is assumed.

scholarly journals ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND EIGENFUNCTIONS OF A NONLOCAL BOUNDARY VALUE PROBLEM

2021 ◽  
Vol 26 (2) ◽  
pp. 253-266
Author(s):  
Erdoğan Şen ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Asymptotic Distribution ◽  
Nonlocal Boundary Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Asymptotic Formulas ◽  
Nonlocal Boundary Value Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Distribution Of Eigenvalues

In this work, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the second order boundary-value problem with a Bitsadze–Samarskii type nonlocal boundary condition.

scholarly journals Existence of solution for Hilfer fractional differential problem with nonlocal boundary condition in Banach spaces

2021 ◽  
Vol 66 (3) ◽  
pp. 521-536
Author(s):  
Hanan A. Wahash ◽  
Mohammed S. Abdo ◽  
Satish K. Panchal ◽  
Sandeep P. Bhairat
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Integral Equation ◽  
Banach Spaces ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Solution ◽  
Existence Of A Solution ◽  
Differential Problem ◽  
Fractional Differential

"This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition in Banach spaces. We use the equivalent integral equation to study the considered Hilfer differential problem with nonlocal boundary condition. The Monch type fixed point theorem and the measure of the noncompactness technique are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example."

scholarly journals The Existence of Multiple Solutions for Boundary Value Problem with One Dimensional p-Laplacian

2013 ◽  
Vol 54 (1) ◽  
pp. 153-163
Author(s):  
Boris Rudolf
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Growth Condition ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Existence Of A Solution ◽  
One Dimensional

Abstract The boundary value problem for a differential equation with one dimensional p-Laplacian is studied. The technique of lower and upper solutions is used. The existence of a solution for well ordered and unordered case as well as the existence of multiple solutions are proved. The growth condition is assumed only on a part of the nonlinearity.

scholarly journals Fučik Spectrum for the Second Order BVP with Nonlocal Boundary Condition

2007 ◽  
Vol 12 (3) ◽  
pp. 419-429 ◽  
Author(s):  
N. Sergejeva
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Fucik Spectrum

We construct the Fučik spectrum for some second order boundary value problem with nonlocal boundary condition. This spectrum differs essentially from the known Fučik spectra. We apply this result to the second order differential equation x'' + g(x) = f(t, x, x') with the conditions x(a) = 0, ∫ab x(s)ds = 0.

scholarly journals Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hongliang Gao ◽  
Xiaoling Han
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary conditionD0+αu(t)+a(t)f(t,u(t))=0,0<t<1,u(0)=0,u(1)=∑i=1∞αiu(ξi)is considered, where1<α≤2is a real number,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),  αi∈[0,∞)with∑i=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

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