Section: New Results

Other new results

In [9], [20], D. Bonheure, J.-B. Casteras and collaborators made bifurcation analysis and constructed multi-layer solutions of the Lin-Ni-Takagi and Keller-Segel equations, which come from the Keller-Segel system of chemotaxis in specific cases. A remarkable feature of the results is that the layers do not accumulate to the boundary of the domain but satisfy an optimal partition problem contrary to the previous type of solutions constructed for these models.

In [10], [23], J.-B. Casteras and collaborators study different problems related to the existence of $A$-harmonic functions with prescribed asymptotic boundary on Cartan-Hadamard manifold. In particular, they obtained a sharp lower bound on the section curvature for the existence of minimal graphic functions with prescribed asymptotic boundary.

In [25], a kinetic equation of the Vlasov-Wave type is studied, which arises in the description of the behavior of a large number of particles interacting weakly with an environment. Variational techniques are used to establish the existence of large families of stationary states for this system, and analyze their stability.