In this paper, we study the problem equation presented where B1 is the unit ball of R2, f is a smooth nonlinearity and α, λ are real numbers with α > 0. From a careful study of the linearized operator, we compute the Morse index of some radial solutions to (P). Moreover, using the bifurcation theory, we prove the existence of branches of nonradial solutions for suitable values of the positive parameter λ. The case f(λ,u) = λeu provides more detailed informations.
Symmetry breaking and Morse index of solutions of nonlinear elliptic problems in the plane / Gladiali, Francesca; Grossi, Massimo; Neves, Sérgio L. N.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 18:5(2016), p. 1550087. [10.1142/S021919971550087X]
Symmetry breaking and Morse index of solutions of nonlinear elliptic problems in the plane
Gladiali, Francesca
;
2016-01-01
Abstract
In this paper, we study the problem equation presented where B1 is the unit ball of R2, f is a smooth nonlinearity and α, λ are real numbers with α > 0. From a careful study of the linearized operator, we compute the Morse index of some radial solutions to (P). Moreover, using the bifurcation theory, we prove the existence of branches of nonradial solutions for suitable values of the positive parameter λ. The case f(λ,u) = λeu provides more detailed informations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
