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Trombetta, Alessandro

A note on symmetry of solutions for a class of singular semilinear elliptic problems. (English) Zbl 1343.35009

Adv. Nonlinear Stud. 16, No. 3, 499-507 (2016).
Summary: We prove symmetry and monotonicity properties for positive solutions of the singular semilinear elliptic equation \[ -\Delta u=\frac{g(x)}{u^{\gamma}}+h(x)f(u) \] in bounded smooth domains with zero Dirichlet boundary conditions. The well-known moving plane method is applied.

Cited in 5 Documents

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35J61 Semilinear elliptic equations
35J75 Singular elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B09 Positive solutions to PDEs

Keywords:

moving plane method; symmetry and monotonicity properties; zero Dirichlet boundary conditions
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References:

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