On the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points
Abdou Kouider Ben-Naoum · Bulletin of the Belgian Mathematical Society - Simon Stevin · 1996
Using Mawhin's coincidence topological degree arguments and fixed point theory for non-expansive mappings results, we discuss the solvability of the Dirichlet problem for the semilinear equation of the vibrating string u xxu yy + f (x, y, u) = 0 in bounded domain with corner points.When the winding number associated to the domain is rational, we improve and extend some results of Lyashenko [8] and Lyashenko-Smiley [9].The case where the winding number is irrational is also examined.