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On the existence of solutions for some nondegenerate nonlinear wave equations of Kirchhoff type

Jong Yeoul Park, Jeong Ja Bae (2002)

Czechoslovak Mathematical Journal

Let Ω be a bounded domain in n with a smooth boundary Γ . In this work we study the existence of solutions for the following boundary value problem: 2 y t 2 - M Ω | y | 2 d x Δ y - t Δ y = f ( y ) in Q = Ω × ( 0 , ) , . 1 y = 0 in Σ 1 = Γ 1 × ( 0 , ) , M Ω | y | 2 d x y ν + t y ν = g in Σ 0 = Γ 0 × ( 0 , ) , y ( 0 ) = y 0 , y t ( 0 ) = y 1 in Ω , ( 1 ) where M is a C 1 -function such that M ( λ ) λ 0 > 0 for every λ 0 and f ( y ) = | y | α y for α 0 .

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