Abstract
For a given bounded domain Ω in R N with smooth boundary ∂Ω, we give sufficient conditions on f so that the m-Laplacian equation △ m u = f(x, u, ∇u) admits a boundary blow-up solution u ∈ W 1,p (Ω). Our main results are new and extend the results in J.V. Concalves and Angelo Roncalli [Boundary blow-up solutions for a class of elliptic equations on a bounded domain, Appl. Math. Comput. 182 (2006), pp. 13–23]. Our approach employs the method of lower–upper solution theorem, fixed point theory and weak comparison principle.
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