Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

Change of Variables as Borel Resummation of Semiclassical Series

It is shown that a change of variable in 1-dim Schrödinger equation applied to the Borel summable fundamental solutions [8, 9] is equivalent to Borel resummation of the fundamental solutions multiplied by suitably chosen h̄-dependent constant. This explains why change of variable can improve JWKB formulae [11]. It is shown also that a change of variable alone cannot provide us with the exact JWK...

STABILITY OF POSITIVE SOLUTIONS TO p&2–LAPLACE TYPE EQUATIONS

In this article, we first show the existence of a positive solution to { −Δpu−αΔu = λ(u− f (u)) in Ω, u = 0 on ∂Ω, by the method of lower and upper solutions and then under certain conditions on f , we show the stability of positive solution. Mathematics subject classification (2010): 35J92, 35B35, 35B05.

A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions

A pr 2 00 6 Positive solutions to nonlinear p - Laplace equations with Hardy potential in exterior domains

We study the existence and nonexistence of positive (super) solutions to the nonlinear p-Laplace equation −∆pu− μ |x|p u = C |x|σ u in exterior domains of R (N ≥ 2). Here p ∈ (1,+∞) and μ ≤ CH , where CH is the critical Hardy constant. We provide a sharp characterization of the set of (q, σ) ∈ R such that the equation has no positive (super) solutions. The proofs are based on the explicit const...

Formal solutions of stargenvalue equations

The formal solution of a general stargenvalue equation is presented, its properties studied and a geometrical interpretation given in terms of star-hypersurfaces in quantum phase space. Our approach deals with discrete and continuous spectra in a unified fashion and includes a systematic treatment of non-diagonal stargenfunctions. The formalism is used to obtain a complete formal solution of Wi...