Balls and Quasi-Metrics: A Space of Homogenous Type Modeling the Real Analysis Related to the Monge-Ampère Equation.
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
A bifurcation problem for the equation in a bounded domain in with mixed boundary conditions, given nonnegative functions and a small perturbation is considered. The existence of a global bifurcation between two given simple eigenvalues of the Laplacian is proved under some assumptions about the supports of the functions . These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to .
We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.