Abstract
We study second and fourth order semilinear elliptic equations with a power-type nonlinearity depending on a power p and a parameter λ > 0 . For both equations we consider Dirichlet boundary conditions in the unit ball B ⊂ R n . Regularity of solutions strictly depends on the power p and the parameter λ . We are particularly interested in the radial solutions of these two problems and many of our proofs are based on an ordinary differential equation approach.
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