Nonlinear Transmission Problems On General Domains

The scattering problem of time harmonic wave is given after its interaction with the obstacle in three dimensions.The mathmatical formulation of this problem involves Helmholtz equations with boundary value conditions at the interface.Under some assumptions on F(x,U),it can be reduced to study the semilinear Helmholtz equation:â–³u + k₁²u = f(x,u)。Here,the existence of solution of the scattering problem on general domains is discussed when f(x,u) =∣u∣^'σu.