Boundary blow-up solutions for a class of quasilinear elliptic equations

For a given bounded domain Omega in R-N with smooth boundary partial derivative Omega, we give sufficient conditions on f so that the m-Laplacian equation Delta(m)u=f(x, u, del u) admits a boundary blow-up solution u is an element of W-1,W-p(Omega). 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.