Jong Yeoul Park

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We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: utt(t,x)− ( α+β (∫ Ω |∇u(t,y)|2dy )γ) ∆u(t,x) −λ∆ut(t,x)+μ|u(t,x)|q−1u(t,x)= 0, x ∈Ω, t ≥ 0, u(0,x)=u0(x), ut(0,x)=u1(x), x ∈Ω, u|∂Ω = 0, where q > 1, λ > 0, μ ∈R, α, β≥ 0, α+β > 0, and ∆ is the Laplacian in RN .
By using a fixed-point theorem in G-convex spaces due to the first author, an existence result for abstract nonlinear inequalities without any monotonicity assumptions is established. As a consequence of our result, we obtain some further generalizations of recent known results. As application, an existence theorem for perturbed saddle point problems is(More)