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Sobolev type embedding and quasilinear elliptic equations with radial potentials. (English) Zbl 1206.35243
Summary: We study the existence of nontrivial radial solutions for quasilinear elliptic equations with unbounded or decaying radial potentials. The existence results are based upon several new embedding theorems we establish in the paper for radially symmetric functions.
MSC:
35R05PDEs with discontinuous coefficients or data
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35J20Second order elliptic equations, variational methods
35J62Quasilinear elliptic equations
58C20Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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