On general solvability properties of \(p\)-Laplacian-like equations. (English) Zbl 1030.35058

Drábek, Pavel; Simader, Christian G.

Math. Bohem. 127, No. 1, 103-122 (2002).

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 \(\Omega = \mathbb R ^N\).

MSC:

35J60	Nonlinear elliptic equations
35J20	Variational methods for second-order elliptic equations

Keywords:

quasilinear elliptic equations; weak solutions; solvability; existence; uniqueness