We study second and fourth order semilinear elliptic equations with a power-type nonlinearity depending on a power p and a parameter $\lambda>0$. For both equations we consider Dirichlet boundary conditions in the unit ball $B\subset\R^n$. Regularity of solutions strictly depends on the power p and the parameter $\lambda$. We are particularly interested in radial solutions of these two problems and many of our proofs are based on an ordinary differential equations approach
Ferrero, A., Warnault, G. (2009). On solutions of second and fourth order elliptic equations with power-type nonlinearities. NONLINEAR ANALYSIS, 70(8), 2889-2902 [10.1016/j.na.2008.12.041].
On solutions of second and fourth order elliptic equations with power-type nonlinearities
FERRERO, ALBERTO;
2009
Abstract
We study second and fourth order semilinear elliptic equations with a power-type nonlinearity depending on a power p and a parameter $\lambda>0$. For both equations we consider Dirichlet boundary conditions in the unit ball $B\subset\R^n$. Regularity of solutions strictly depends on the power p and the parameter $\lambda$. We are particularly interested in radial solutions of these two problems and many of our proofs are based on an ordinary differential equations approach
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