Nonhomogeneous boundary value problem for a semilinear hyperbolic equation

Volume 35 / 2008

Andrzej Nowakowski Applicationes Mathematicae 35 (2008), 81-95 MSC: Primary 35L05, 35L20; Secondary 35A15. DOI: 10.4064/am35-1-5


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.


  • Andrzej NowakowskiFaculty of Mathematics
    University of /L/od/x
    Banacha 22
    90-238 /L/od/x, Poland

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