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Semilinear elliptic problems


The semilinear elliptic problems lie at the heart of the theory of elliptic partial differential equations. A better understanding of these problems results in a deeper knowledge of this theory and permits us to treat more complex problems such as quasilinear problems and elliptic systems. In recent years, there has been a remarkable progress in the theory, however there are still many open questions. In this project, we approach some semilinear problems like the ones with type concave-convex and/or gradient, and resonant linearities, under different boundary conditions. The acquired background allows us also to deal with quasilinear problems. The main focus is the achievement of existence and multiplicity results. To attain this goal, we create, adapt and combine techniques, which supply new tools to the contemporary research. (AU)

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(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
PRESOTO, ADILSON EDUARDO; DE PAIVA, FRANCISCO ODAIR. A Neumann problem of Ambrosetti-Prodi type. Journal of Fixed Point Theory and Applications, v. 18, n. 1, p. 189-200, MAR 2016. Web of Science Citations: 5.

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