TY - JOUR
AU - García-Melián, J.
AU - Rossi, J.D.
AU - Sabina de Lis, J.C.
T1 - Multiplicity of solutions to a nonlinear elliptic problem with nonlinear boundary conditions
LA - eng
PY - 2014
SP - 305
EP - 337
T2 - Nonlinear Differential Equations and Applications
SN - 1420-9004
VL - 21
IS - 3
PB - Birkhauser Verlag AG
AB - We study the problem (Formula presented.) where Ω ⊂ ℝN is a bounded smooth domain, ν is the outward unit normal at ∂Ω and λ > 0 is regarded as a bifurcation parameter. When p = 2 and in the superlinear regime q > 2, we show existence of n nontrivial solutions for all λ > λn, λn being the n-th Steklov eigenvalue. It is proved in addition that bifurcation from the trivial solution takes place at all λn 's. Similar results are obtained in the sublinear case 1 < q < 2. In this case, bifurcation from infinity takes place in those λn with odd multiplicity. Partial extensions of these features are shown in the nonlinear diffusion case p ≠ 2 and related problems under spatially heterogeneous reactions are also addressed. © 2013 Springer Basel.
DO - 10.1007/S00030-013-0248-8
UR - https://portalciencia.ull.es/documentos/5e3c39ac29995246bbf5f5a0
DP - Dialnet - Portal de la Investigación
ER -