Global existence of weak solutions to the boundary value problem for a three-dimensional viscoelastic dynamic system

1996 ◽  
Vol 42 (2) ◽  
pp. 99-114 ◽  
Author(s):  
Oin Tiehu
Keyword(s):  
Global Existence ◽  
Boundary Value Problem ◽  
Dynamic System ◽  
Weak Solutions ◽  
Boundary Value ◽  
Three Dimensional ◽  
Existence Of Weak Solutions

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.

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.

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