Pseudo-monotonicity and degenerated or singular elliptic operators. (English) Zbl 0913.35051
Summary: Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The results extends analogous assertions for elliptic operators.
MSC:
35J70 | Degenerate elliptic equations |
47J25 | Iterative procedures involving nonlinear operators |
35J60 | Nonlinear elliptic equations |
References:
[1] | Opic, Hardy-type inequalities 219 (1990) |
[2] | Drábek, Quasilinear elliptic equations with degenerations and singularities 5 (1997) · Zbl 0894.35002 · doi:10.1515/9783110804775 |
[3] | Gossez, Differential Integral Equations 6 pp 37– (1993) |
[4] | Mustonen, Theory and applications of nonlinear operators of acretive and monotone type 178 pp 215– (1996) |
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