Indefinite Quasilinear Neumann Problem on Unbounded Domains

Volume 54 / 2006

J. Chabrowski Bulletin Polish Acad. Sci. Math. 54 (2006), 207-217 MSC: 35B33, 35J20, 35J65. DOI: 10.4064/ba54-3-3


We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain $\mit\Omega$. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.


  • J. ChabrowskiDepartment of Mathematics
    University of Queensland
    St. Lucia 4072, Qld, Australia

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