2 resultados para Critical Sequence

em Biblioteca Digital da Produção Intelectual da Universidade de São Paulo (BDPI/USP)


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Mobius sequence is a congenital facial and abducens nerve palsy, frequently associated to abnormalities of extremities. Arthrogryposis multiplex congenital is defined as a congenital fixation of multiple joints seldom of neurogenic origin. Both sequences must have a genetic origin, but usually are sporadic cases related to environmental factors such as drugs exposition and maternal trauma. A 5-year-old girl and a 1-year-old boy were born with Mobius sequence and arthrogryposis multiplex congenital, respectively. During pregnancies, the mother had vaginal bleeding at 7 weeks and used crack (free-based cocaine) in the first trimester, respectively. The girl also has equinovarus talipes and autistic behavior. The boy has arthrogryposis with flexion contractures of the feet and knees. A vascular disruption, due to hemorrhage and cocaine exposure, causing a transient ischemic insult to embryos in a critical period of development may be responsible for distinct phenotypes in these cases.

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In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.