ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We consider the existence of weak solutions of the periodic-Dirichlet problem on ]0, 2π[×]0, π[for the semi-linear wave equation u tt -uv xx -f(t, x, u=0 when x(t, x)⩽lim in u −1 f(t, x, u)⩽lim supu −1 f(t, x, u) ⩽ Β(t, x ¦u¦→∞ ¦u¦→∞ and α and Β satisfy some nonresonance conditions of non uniform type withr espect to two consecutive nonzero eigenvalues of the associated linear problem. The proof is based upon one generalized continuation theorem for some perturbations of mappings which are not of Fredholm type.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01781063
Permalink