On p-biharmonic equations with critical growth / Sobre equações p-biharmónicas com crescimento crítico

We study p-biharmonic problems dealing with concave-convex nonlinearities in the critical case with both Navier and Dirichlet boundary conditions in a bounded, smooth domain and some f ? C(?), which is either a positive or a change-sign function. By applying Nehari’s minimization method, we prove the existence of two nontrivial solutions for the problems. If f is positive, both solutions of the problem with Navier boundary condition are positive

Teoremas de minimização para funcionais não-suaves sobre espaços de aplicações

Exportado OPUSMade available in DSpace on 2019-08-14T13:56:56Z (GMT). No. of bitstreams: 1 diss182.pdf: 522273 bytes, checksum: 8d9f41db927fe0d79a6b89c1631919ce (MD5) Previous issue date: 17Nesta dissertação, estendemos o lema de Brézis-Lieb e o princípio de Concentração e Compacidade a um contexto vetorial sobre espaços de aplicações. É importante salientar que este é um resultado essencial em toda a dissertação. Finalizamos nosso trabalho exibindo algumas condições simples de serem verificadas sobre F e G tal que as hipóteses dos principais teoremas desta dissertação são satisfeitas.In this thesis, we extend lemma Brézis-Lieb and the principle of Concentration Compactness and the context of vector spaces applications. It is important to note that this is an essential result in the entire paper. We finish our work by displaying some simple conditions to be verified over F and G such that the hypothesis of the main theorems of this work are met

Multiplicidade de soluções para problemas com condições de fronteira de Dirichlet e Navier envolvendo o operador p-biharmônico com expoente crítico

Exportado OPUSMade available in DSpace on 2019-08-12T17:28:45Z (GMT). No. of bitstreams: 1 tese061.pdf: 732921 bytes, checksum: c038e85766b71c85337a00e2dfc13156 (MD5) Previous issue date: 6Nos dois capítulos apresentamos, desse modo, uma generalização para o operador p-biharmônico do trabalho de Bernis, García-Azorero e Peral [5], que trata do operador biharmônico. Naquele trabalho, o método de sub- e supersolução é utilizado. Em nosso primeiro capítulo não utilizamos esse método e sim o método da variedade de Nehari, aplicando o lema de Lions. (Nessa generalização, incluímos uma função peso f que pode trocar de sinal (em [5] é como se a função peso f fosse igual a 1). No segundo capítulo, adaptamos ao operador p-biharmônico o método de Ljusternik-Schnirelmann utilizado no artigo de Bernis, García-Azorero e Peral

Ceratocystis cacaofunesta genome analysis reveals a large expansion of extracellular phosphatidylinositol-specific phospholipase-C genes (PI-PLC)

Background: The Ceratocystis genus harbors a large number of phytopathogenic fungi that cause xylem parenchyma degradation and vascular destruction on a broad range of economically important plants. Ceratocystis cacaofunesta is a necrotrophic fungus responsible for lethal wilt disease in cacao. The aim of this work is to analyze the genome of C. cacaofunesta through a comparative approach with genomes of other Sordariomycetes in order to better understand the molecular basis of pathogenicity in the Ceratocystis genus. Results: We present an analysis of the C. cacaofunesta genome focusing on secreted proteins that might constitute pathogenicity factors. Comparative genome analyses among five Ceratocystidaceae species and 23 other Sordariomycetes fungi showed a strong reduction in gene content of the Ceratocystis genus. However, some gene families displayed a remarkable expansion, in particular, the Phosphatidylinositol specific phospholipases-C (PI-PLC) family. Also, evolutionary rate calculations suggest that the evolution process of this family was guided by positive selection. Interestingly, among the 82 PI-PLCs genes identified in the C. cacaofunesta genome, 70 genes encoding extracellular PI-PLCs are grouped in eight small scaffolds surrounded by transposon fragments and scars that could be involved in the rapid evolution of the PI-PLC family. Experimental secretome using LC-MS/MS validated 24% (86 proteins) of the total predicted secretome (342 proteins), including four PI-PLCs and other important pathogenicity factors. Conclusion: Analysis of the Ceratocystis cacaofunesta genome provides evidence that PI-PLCs may play a role in pathogenicity. Subsequent functional studies will be aimed at evaluating this hypothesis. The observed genetic arsenals, together with the analysis of the PI-PLC family shown in this work, reveal significant differences in the Ceratocystis genome compared to the classical vascular fungi, Verticillium and Fusarium. Altogether, our analyses provide new insights into the evolution and the molecular basis of plant pathogenicity. © 2018 The Author(s)