We prove the existence of nonradial solutions for the H'enon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent $alpha$. For sign-changing solutions, the case $alpha=0$ -- Lane-Emden equation -- is included. The obtained solutions form global continua which branch off from the curve of radial solutions $pmapsto u_p$, and the number of branching points increases with both the number of nodal zones and the exponent $alpha$. The proof technique relies on the index of fixed points in cones and provides information on the symmetry properties of the bifurcating solutions and the possible intersection and/or overlapping between different branches, thus allowing to separate them at least in some cases.
Global bifurcation for the Hénon problem
Anna Lisa Amadori
2020-01-01
Abstract
We prove the existence of nonradial solutions for the H'enon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent $alpha$. For sign-changing solutions, the case $alpha=0$ -- Lane-Emden equation -- is included. The obtained solutions form global continua which branch off from the curve of radial solutions $pmapsto u_p$, and the number of branching points increases with both the number of nodal zones and the exponent $alpha$. The proof technique relies on the index of fixed points in cones and provides information on the symmetry properties of the bifurcating solutions and the possible intersection and/or overlapping between different branches, thus allowing to separate them at least in some cases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.