Publications (8) View all
-
Article: The Use of Cerami Sequences in Critical Point Theory
[show abstract] [hide abstract]
ABSTRACT: The concept of linking was developed to produce Palais-Smale (PS) sequences G(uk)→a, G'(uk)→0 for C1functionals G that separate linking sets. These sequences produce critical points if they have convergent subsequences (i.e., if G satisfies the PS condition). In the past, we have shown that PS sequences can be obtained even when linking does not exist. We now show that such situations produce more useful sequences. They not only produce PS sequences, but also Cerami sequences satisfying G(uk)→a, (1+||uk||)G'(uk)→ 0 as well. A Cerami sequence can produce a critical point even when a PS sequence does not. In this situation, it is no longer necessary to show that G satisfies the PS condition, but only that it satisfies the easier Cerami condition (i.e., that Cerami sequences have convergent subsequences). We provide examples and applications. We also give generalizations to situations when the separating criterion is violated.Abstract and Applied Analysis. 01/2007; -
Article: Periodic solutions of second-order nonautonomous dynamical systems
[show abstract] [hide abstract]
ABSTRACT: We study the existence of periodic solutions for second-order nonautonomous dynamical systems. We give four sets of hypotheses which guarantee the existence of solutions. We were able to weaken the hypotheses considerably from those used previously for such systems. We employ a new saddle point theorem using linking methods.Boundary Value Problems. 01/2006; -
Article: Finding linking sets
[show abstract] [hide abstract]
ABSTRACT: We present the most general definition of the linking of sets in a Banach space and discuss necessary and sufficient conditions for sets to link.International Journal of Mathematics and Mathematical Sciences. 01/2006; -
Article: Semilinear problems with bounded nonlinear term
[show abstract] [hide abstract]
ABSTRACT: We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term.Boundary Value Problems. 01/2005; -
Article: Semilinear elliptic equations having asymptotic limits at zero and infinity
[show abstract] [hide abstract]
ABSTRACT: We obtain nontrivial solutions for semilinear elliptic boundary value problems having resonance both at zero and at infinity, when the nonlinear term has asymptotic limits.Abstract and Applied Analysis. 01/1999;
