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

No hay miniatura disponible
Ma Y.
Wang Y.
Ledesma C.T.
Título de la revista
Revista ISSN
Título del volumen
De Gruyter Open Ltd
Proyectos de investigación
Unidades organizativas
Número de la revista
Our purpose of this paper is to study positive solutions of Lane-Emden equation -?u=Vup in RN0 perturbed by a non-homogeneous potential V when p ? [pc,N+2N-2), where pc is the Joseph-Ludgren exponent. When p ? (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 -?u = up in RN \ 0 by authors in [9]. While the fast decaying solution wk is unstable for p ? (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 -?u=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. © 2021 Yong Ma et al., published by De Gruyter 2021.
Y. Ma is supported by Key R&D plan of Jiangxi Province, No:20181ACE50029, Y. Wang is supported by NNSF of China, No:12001252 and 12071189, by the Jiangxi Provincial Natural Science Foundation, No:20202ACBL201001 and 20202BAB201005, by the Science and Technology Research Project of Jiangxi Provincial Department of Education, No: 200325 and 200307, C. Torres was partially supported by CONCYTEC, Peru, 379-2019-FONDECYT “ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES”
Palabras clave
Singularity, Decaying Solution, Lane-Emden Equation, Potential