Systems of partial differential equations and nonlinear elliptic equations

Abstract

In the period of the visit of Professor Ubilla to the UNICAMP we will continue our research in the area of Partial Differential Equations, studying: 1) Hamiltonian Systems, 2) Nonlinear Differential Equations, mostly the p-Laplacian.For Hamiltonian Systems , we will study the questions of existence and multiplicity of solutions for boundary value problems in bounded domains , as well in the whole space. We will consider the so-called Sobolev case that corresponds to problems in RN with n>=3, and also the Trudinger-Moser case that corresponds to N=2.For Nonlinear Differential Equations, we will continue the research that we have been doing with Jean-Pierre Gossez from the Université Libre de Bruxelles. studying the p-Laplacian with non-homogeneous boundary conditions, and trying to determine the whole of weights in the nonlinearities, in analogy with the work of Ni and others (including the proponent) for the Laplacian.More details in the enclosed Research Project. References: FIGUEIREDO, D.G.; GOSSEZ, J.-P.; UBILLA, P. Local Superlinearity and sublinearity for the p-Laplacian. Journal of Functional Analysis, v. 257, p. 721-752, 2009. FIGUEIREDO, D.G.; LOPEZ, P.U.; Sanchez, J. Quasilinear equations with dependence in the gradient. Nonlinear Analysis, v. 71, p. 4862-4868, 2009. FIGUEIREDO, D.G.; UBILLA, P. SUPERLINEAR SYSTEMS OF SECOND ORDER ODE'S. Nonlinear Analysis. Theory, Methods and Applications, v. 68, p. 1765-1773, 2008. FIGUEIREDO, D.G.; GOSSEZ, J.P.; LOPEZ, P.U. Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity. Journal of the European Mathematical Society, v. 8, p. 269-286, 2006. (AU)