Fredholm alternative and boundary value problems

On Fredholm Alternative for Certain Quasilinear Boundary Value Problems

We study the Dirichlet boundary value problem for the p-Laplacian of the form −∆pu− λ1|u|p−2u = f in Ω, u = 0 on ∂Ω, where Ω ⊂ N is a bounded domain with smooth boundary ∂Ω, N 1, p > 1, f ∈ C(Ω) and λ1 > 0 is the first eigenvalue of ∆p. We study the geometry of the energy functional Ep(u) = 1 p ∫

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Generalized Riemann-hilbert Transmission and Boundary Value Problems, Fredholm Pairs and Bordisms

We present classical and generalized Riemann-Hilbert problem in several contexts arising from K-theory and bordism theory. The language of Fredholm pairs turns out to be useful and unavoidable. We propose an abstract formulation of a notion of bordism in the context of Hilbert spaces equipped with splittings. §

Subelliptic Boundary Value Problems and the G-fredholm Property Preliminary Version

Let G be a unimodular Lie group, X a compact manifold with boundary, and M be the total space of a principal bundle G → M → X so that M is also a complex manifold satisfying a local subelliptic estimate. In this work, we show that if G acts by holomorphic transformations in M , then the Laplacian = ∂̄∗∂̄ + ∂̄∂̄∗ on M has the following properties: The kernel of restricted to the forms Λ with q > 0 i...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation