Existence of positive boundary blow-up solutions for quasilinear elliptic equations via sub and supersolutions. (English) Zbl 1137.35371

Summary: In this paper, the existence of a positive boundary blow-up weak solution for the quasilinear elliptic equation \[ \text{div}(| \nabla u| ^ {p-2}\nabla u)=m(x)f(u) \] in a smooth bounded domain \(\Omega\subset \mathbb R^ N\) as well as on the whole space \(\Omega=\mathbb R^ N\) is obtained under new conditions. Our proof is based on the method of sub- and super-solutions.


35J60 Nonlinear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
Full Text: DOI


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