Alonso, JM
Mawhin, Jean
[UCL]
Ortega, R.
Motivated by the problem of the existence of a solution of the nonlinear telegraph equation
u(tt) + cu(t) - u(xx) + h(t, x, u) = 0,
such that u(t, .) satisfies suitable boundary conditions over (0, pi) and parallel to u(t, .)parallel to is bounded over R for some function space norm parallel to . parallel to, we prove the existence of bounded solutions over R of semilinear evolution equations in a Hilbert space of the form
u + cu + Au + g(t, u) = 0,
where c > 0, A : D(A) subset of H --> H is self-adjoint, semi-positive definite, has compact resolvant and g : R x H --> H, bounded and sufficiently regular satisfies some Landesman-Lazer type condition. (C) Elsevier, Paris.
Bibliographic reference |
Alonso, JM ; Mawhin, Jean ; Ortega, R.. Bounded solutions of second order semilinear evolution equations and applications to the telegraph equation. In: Journal de mathématiques pures et appliquées, Vol. 78, no. 1, p. 49-63 (1999) |
Permanent URL |
http://hdl.handle.net/2078.1/44645 |