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Article

Drábek, Pavel ; Simader, Christian G.
On general solvability properties of $p$-Lapalacian-like equations. (English). Mathematica Bohemica, vol. 127 (2002), issue 1, pp. 103-122
MSC: 35B40, 35J15, 35J20, 35J60 | MR 1895250 | Zbl 1030.35058 | DOI: 10.21136/MB.2002.133987
Keywords:
quasilinear elliptic equations; weak solutions; solvability
Summary:
We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation \[ -\Delta _p u = f \ \text{in} \ \Omega , \] where $\Omega $ is a very general domain in $\mathbb{R}^N$, including the case $\Omega = \mathbb{R}^N$.
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