MATHEMATICA BOHEMICA, Vol. 127, No. 1, pp. 103-122 (2002)

On general solvability properties of $p$-Lapalacian-like equations

Pavel Drabek, Christian G. Simader

Pavel Drabek, Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Plzen, Czech Republic, e-mail:
Christian G. Simader, Mathematisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany, e-mail:

Abstract: 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 \mbox { in } \Omega ,
where $\Omega $ is a very general domain in $\R ^N$, including the case $\Omega = \R ^N$.

Keywords: quasilinear elliptic equations, weak solutions, solvability

Classification (MSC2000): 35J15, 35J20, 35B40

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