Article - postprint
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].
© 1980 Elsevier
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.