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.

Weak solutions for a second order impulsive boundary value problem

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6431-6439
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Donal O’Regan
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Degree Theory ◽  
Point Theory ◽  
Second Order ◽  
Positive Parameter ◽  
Topological Degree Theory ◽  
Existence Of Weak Solutions ◽  
Impulsive Boundary Value Problem

In this paper we use topological degree theory and critical point theory to investigate the existence of weak solutions for the second order impulsive boundary value problem {-x??(t)- ?x(t) = f (t), t ? tj, t ? (0,?), ?x?(tj) = x?(t+j)- x?(t-j) = Ij(x(tj)), j=1,2,..., p, x(0) = x(?) = 0, where ? is a positive parameter, 0 = t0 < t1 < t2 < ... < tp < tp+1 = ?, f ? L2(0,?) is a given function and Ij ? C(R,R) for j = 1,2,..., p.

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.

Existence and Multiplicity of Positive Solutions for a Dirichlet Boundary Value Problem in ℝ2

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
V. Barutello ◽  
A. Capietto ◽  
P. Habets
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Parameter Dependent ◽  
Vector Differential Equation

AbstractWe deal with the Dirichlet boundary value problem associated to a parameter-dependent second order vector differential equation. Using the method of lower and upper solutions together with degree theory, we provide existence and multiplicity of positive solutions.

On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front

2003 ◽  
Vol 10 (3) ◽  
pp. 543-548
Author(s):  
V. A. Kondrat'ev ◽  
V. A. Nikishkin
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Dirichlet Boundary Value Problem ◽  
Asymptotics Of Solutions ◽  
Divergent Form ◽  
Second Order Elliptic Equations

Abstract Two terms of asymptotics near crack are obtained for solutions of the Dirichlet boundary value problem for second-order elliptic equations in divergent form. The front of a crack is from 𝐶1+𝑠 and the coefficients of the equations belong to 𝐶𝑠 (0.5 < 𝑠 < 1).

Elliptic problems in generalized Orlicz-Musielak spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Piotr Gwiazda ◽  
Piotr Minakowski ◽  
Aneta Wróblewska-Kamińska
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Hölder Continuous ◽  
Existence Of Weak Solutions ◽  
Strongly Nonlinear

AbstractWe consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

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