Nonhomogeneous boundary value problem for a semilinear hyperbolic equation
Volume 35 / 2008
Applicationes Mathematicae 35 (2008), 81-95
MSC: Primary 35L05, 35L20; Secondary 35A15.
DOI: 10.4064/am35-1-5
Abstract
We discuss the solvability of a nonhomogeneous boundary value problem for the semilinear equation of the vibrating string $x_{tt}(t,y)-\Delta x(t,y)+f(t,y,x(t,y))=0$ in a bounded domain and with a certain type of superlinear nonlinearity. To this end we derive a new dual variational method.
