TY - JOUR
T1 - On solutions of second and fourth order elliptic equations with power-type nonlinearities
AU - Ferrero, Alberto
AU - Warnault, Guillaume
PY - 2009/4/15
Y1 - 2009/4/15
N2 - 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 ⊂ Rn. 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.
AB - 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 ⊂ Rn. 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.
KW - Dirichlet problem
KW - Fourth order equations
KW - Regularity of solutions
KW - Second order equations
UR - http://www.scopus.com/inward/record.url?scp=61749088402&partnerID=8YFLogxK
U2 - 10.1016/j.na.2008.12.041
DO - 10.1016/j.na.2008.12.041
M3 - Article
SN - 0362-546X
VL - 70
SP - 2889
EP - 2902
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 8
ER -