Nonexistence results of sign-changing solutions to a supercritical nonlinear problem

Existence and nonexistence of sign-changing solutions to elliptic critical equations

“…This result is generalized by Musso and Pistoia in [22], under a suitable assumption on the nondegeneracy of Robin's function. Moreover, Ben Ayed and Ould Bouh in [9] proved that the phenomenon of bubble-tower solutions cannot occur in the supercritical case. In this theorem, we prove that this phenomenon cannot occur in the case where k = 3, in the sense that the distances of the two positive blow-up points from each other and from the boundary are bounded.…”

A Nonexistence of Solutions to a Supercritical Problem

“…However, del Pino et al [6] gave an existence result for two blow up points, provided that Ω satisfies some geometrical conditions. In sharp contrast to this, it proved in [5] for the case K is a constant and [8] for the case K is a non constant function that, for @ small, has no sign-changing solutions which blow up at two points.…”

On a biharmonic equation involving slightly supercritical exponent

“…In this paper, we consider the case in which K is a nonconstant function and we seek to understand the influence of the function K in the study of the sign-changing solutions of (P ε ) . We note that, when the biharmonic operator in (P ε ) is replaced by the Laplacian one, there are many works devoted to the study of the solutions of the counterpart of (P ε ) , for example [3,4,7,9,12,18].…”