Annamaria Canino

A Jumping Problem for Some Singular Semilinear Elliptic Equations

Abstract We consider a jumping problem for singular semilinear elliptic equations. Existence of two distinct solutions is proved via a truncation argument and exploiting minimax methods to prove the existence of solutions to the truncated problem. In the final step, to pass to the limit, a refined analysis about the behavior of the solutions is required, because of the singular nature of the problem.

On the moving plane method for boundary blow-up solutions to semilinear elliptic equations

Abstract We consider weak solutions to - Δ ⁢ u = f ⁢ ( u ) {-\Delta u=f(u)} on Ω 1 ∖ Ω 0 {\Omega_{1}\setminus\Omega_{0}} , with u = c ≥ 0 {u=c\geq 0} in ∂ ⁡ Ω 1 {\partial\Omega_{1}} and u = + ∞ {u=+\infty} on ∂ ⁡ Ω 0 {\partial\Omega_{0}} , and we prove monotonicity properties of the solutions via the moving plane method. We also prove the radial symmetry of the solutions in the case of annular domains.