scholarly journals Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Jigen Peng
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Of Solution ◽  
Dirichlet Boundary Value Problem ◽  
Condensing Mapping

The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

scholarly journals Existence results for a sublinear second order Dirichlet boundary value problem on the half-line

2020 ◽  
Vol 40 (5) ◽  
pp. 537-548
Author(s):  
Dahmane Bouafia ◽  
Toufik Moussaoui
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Half Line ◽  
Dirichlet Boundary Value Problem ◽  
Nontrivial Solutions

In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland's variational principle and critical point theory.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

scholarly journals Dirichlet Problem for Maximal Graphs of Higher Codimension

2020 ◽  
Author(s):  
Yang Li
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
General Existence

Abstract We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian-type ambient spaces and obtain general existence and uniqueness results that apply to any codimension.

scholarly journals Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shaohong Wang ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Strong Maximum Principle ◽  
Dirichlet Boundary Value Problem ◽  
Partial Difference Equation ◽  
Three Solutions ◽  
Partial Difference

AbstractBy employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give precise estimates of the parameter to guarantee that the considered problem possesses at least three solutions. Furthermore, based on a strong maximum principle, we show that two of the obtained solutions are positive under some suitable assumptions of the nonlinearity.

scholarly journals Weak Solutions for a Second Order Dirichlet Boundary Value Problem on Time Scale

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wandong Lou
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Existence Theorems ◽  
Boundary Value ◽  
Degree Theory ◽  
Point Theory ◽  
Second Order ◽  
Dirichlet Boundary Value Problem

We adopt the Leray-Schauder degree theory and critical point theory to consider a second order Dirichlet boundary value problem on time scales and obtain some existence theorems of weak solutions for the previous problem.

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