| Full text | |
| Author(s): |
Ramos Quoirin, Humberto
;
Siciliano, Gaetano
;
Silva, Kaye
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Nonlinearity; v. 37, n. 6, p. 40-pg., 2024-06-03. |
| Abstract | |
We look for critical points with prescribed energy for the family of even functionals Phi mu = I-1 - mu I-2 , where I-1, I-2 are C-1 functionals on a Banach space X, and mu is an element of R . For a given c is an element of R and several classes of Phi(mu), we prove the existence of infinitely many couples (mu(n,c) , u(n,c)) such that Phi(mu n,c)' (+/- u(n,c)) = 0 and Phi(mu n,c) (+/- u(n,c)) = c for all n is an element of N. More generally, we analyse the structure of the solution set of the problem Phi(mu)'(u) = 0 , Phi(mu) (u) = c with respect to mu and c. In particular, we show that the maps c bar right arrow mu(n,c) are continuous, which gives rise to a family of energy curves for this problem. The analysis of these curves provide us with several bifurcation and multiplicity type results, which are then applied to some elliptic problems. Our approach is based on the nonlinear generalized Rayleigh quotient method developed in Il'yasov (2017 Topol. Methods Nonlinear Anal. 49 683-714). (AU) | |
| FAPESP's process: | 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Research Projects - Thematic Grants |