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 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.

scholarly journals Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hua Luo
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scale ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Bifurcation From Interval

Let𝕋be a time scale with0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale𝕋,uΔΔ(t)+f(t,uσ(t))=0,  t∈[0,T]𝕋,  u(0)=u(σ2(T))=0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.

scholarly journals Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 475 ◽  
Author(s):  
Fares Kamache ◽  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Asma Alharbi
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Existence Of Weak Solutions ◽  
New Class ◽  
Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

scholarly journals Weak Solutions for ap-Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Wei Dong
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Point Theory ◽  
Existence Of Weak Solutions

By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for ap-Laplacian impulsive differential equation with antiperiodic boundary conditions.

scholarly journals On a class of second-order impulsive boundary value problem at resonance

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Guolan Cai ◽  
Zengji Du ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
General Theorem ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Impulsive Boundary Value Problem ◽  
Problem At Resonance

We consider the following impulsive boundary value problem,x″(t)=f(t,x,x′),t∈J\{t1,t2,…,tk},Δx(ti)=Ii(x(ti),x′(ti)),Δx′(ti)=Ji(x(ti),x′(ti)),i=1,2,…,k,x(0)=(0),x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usualm-point boundary value problem at resonance without impulses.

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