E. N. Dancer

On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem

We discuss the existence of positive solutions of some singularity perturbed elliptic equations on convex domains with nonlinearity changing sign. In particular, we obtain solutions with both a boundary layer and a sharp interior peak.

Some remarks on Liouville type results for quasilinear elliptic equations

For a wide class of nonlinearities f(u) satisfying f(0) = f(a) = 0, f(u) > 0 in (0, a) and f(u) < 0 in (a, ∞), we show that any nonnegative solution of the quasilinear equation -Δ p u = f(u) over the entire R N must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

A Liouville theorem for p-harmonic functions on exterior domains

We prove Liouville type theorems for

DOMAIN PERTURBATION FOR ELLIPTIC EQUATIONS SUBJECT TO ROBIN BOUNDARY CONDITIONS

p

A Note on Multiple Solutions of Some Semilinear Elliptic Problems

p-harmonic functions on exterior domains of

On a free boundary problem arising from population biology

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