| Full text | |
| Author(s): |
Luna, T. L. M.
;
Carvalho, A. N.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 373, p. 30-pg., 2023-11-15. |
| Abstract | |
In this paper we study the existence of solutions of a one-dimensional eigenvalue problem -(|& phi;x|p-2 & phi;x)x = & lambda; |& phi;|q-2 & phi; - f (& phi;) such that & phi;(0) = & phi;(1) = 0, where p, q > 1, & lambda; is a positive real parameter and f is a continuous (not necessarily odd) function. Our goal is to give a complete description of solutions of this problem. We completely characterize the set of solutions of this problem, which may be uncountable. For 1 < p = 2, the existing results treat only the case when f is either odd and a power (see [11]) or when p = q ([8]). Our method of proof relies on a careful analysis of the phase diagram associated with this equation, refining the regularity results of M. Otani in 1984 (see [10]) and characterizing the exact points where we may have C2 regularity of solutions including some points & chi; & ISIN; (0, 1) for which & phi;x (& chi; ) = 0. & COPY; 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 19/20341-3 - Asymptotic analysis of autonomous and non-autonomous parabolic problems |
| Grantee: | Tito Luciano Mamani Luna |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |