Radial solutions for Hénon type fully nonlinear equations in annuli and exterior domains

Multiple Positive Radial Solutions for Quasilinear Equations in Annular Domains

Positive Super-solutions to Semi-linear Second-order Non-divergence Type Elliptic Equations in Exterior Domains

We study the problem of the existence and non-existence of positive super-solutions to a semi-linear second-order non-divergence type elliptic equation ∑N i,j=1 aij(x) ∂2u ∂xi∂xj + up = 0, −∞ < p < ∞, with measurable coefficients in exterior domains of RN . We prove that in a “generic” situation there is one critical value of p that separates the existence region from nonexistence. We reveal th...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Non-existence of Positive Solutions of Fully Nonlinear Elliptic Equations in Unbounded Domains

In this paper we consider fully nonlinear elliptic operators of the form F (x, u,Du,D2u). Our aim is to prove that, under suitable assumptions on F , the only nonnegative viscosity super-solution u of F (x, u,Du,D2u) = 0 in an unbounded domain Ω is u ≡ 0. We show that this uniqueness result holds for the class of nonnegative super-solutions u satisfying inf x∈Ω u(x) + 1 dist(x, ∂Ω) = 0, and the...