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.
Acknowledgements
This project was supported by the National Natural Science Foundation of China (Grant No. 10871060) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110005).