On Picard-Fuchs type equations related to integrable Hamiltonian systems.
We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems where is the -Laplace operator, and is a -domain in . We prove an analogue of [7, 16] for the eigenvalue problem with , and obtain a non-existence result of positive solutions for the general systems.
We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.