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Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations. (English) Zbl 1200.35143
Summary: We study weighted Sobolev embeddings in radially symmetric function spaces and then investigate the existence of nontrivial radial solutions of inhomogeneous quasilinear elliptic equation with singular potentials and super-\((p,q)\)-linear nonlinearity. The model equation is of the form
\[ \begin{cases} -\Delta_p u+V(|x|)|u|^{q-2}u= Q(|x|)|u|^{s-2}u, &x\in\mathbb R^N,\\ u(x) \rightarrow 0, \quad\text{as}\quad |x|\rightarrow\infty. \end{cases} \]

MSC:
35J62 Quasilinear elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J20 Variational methods for second-order elliptic equations
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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