Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case

Ma Y.; Wang Y.; Ledesma C.T. · Advances in Nonlinear Analysis (2021) · DOI: 10.1515/anona-2020-0129

Resumen

Our purpose of this paper is to study positive solutions of Lane-Emden equation -Δu=Vup in RN0 perturbed by a non-homogeneous potential V when p ϵ [pc,N+2N-2), where pc is the Joseph-Ludgren exponent. When p ϵ (NN-2,pc) the fast decaying solution could be approached by super and sub solutions, which are constructed by the stability of the k-fast decaying solution wk of -Δu = up in RN \ 0 by authors in [9]. While the fast decaying solution wk is unstable for p ϵ (pc,N+2N-2) so these fast decaying solutions seem not able to disturbed like (0.1) by non-homogeneous potential V. A surprising observation that there exists a bounded sub solution of (0.1) from the extremal solution of -Δu=uN+2N-2 in RN and then a sequence of fast decaying solutions and slow decaying solutions could be derived under appropriated restrictions for V.

Instituciones: Universidad Nacional de Trujillo