Document Type
Article - postprint
Department
Mathematics (HMC)
Publication Date
11-1980
Abstract
In this paper, we study the existence of weak solutions of the problem
□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)
u(t,x) = 0 ; (t,x) є ∂Ω
where □ is the wave operator ∂2/∂t2 - ∂2/∂x2, G: Rn→R is a function of class C2 such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L2,(Ω))n and satisfying
f(0,x) = f(π,x) = 0
for all x є [0,π].
Rights Information
© 1980 Elsevier
Terms of Use & License Information
DOI
10.1016/0362-546X(80)90024-3
Recommended Citation
Bates, Peter W. and Alfonso Castro. “Existence and uniqueness for a variational hyperbolic system without resonance” Nonlinear Analysis TMA, Vol. 4, No. 6(1980), pp. 1151-1156.
Included in
Mathematics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons
Comments
Author's post-print manuscript available for download.
For the publisher's PDF, please visit http://dx.doi.org/10.1016/0362-546X(80)90024-3.