Comparison principle for some classes of nonlinear elliptic equations

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...

Some nonlinear elliptic equations from geometry.

We describe some recent work on certain nonlinear elliptic equations from geometry. These include the problem of prescribing scalar curvature on (n), the Yamabe problem on manifolds with boundary, and the best Sobolev inequality on Riemannian manifolds.

Comparison Theorems for Special Classes of Nonselfadjoint Elliptic Equations

Known comparisons for nonselfadjoint elliptic equations are strengthened in cases where the coefficients of these equations satisfy special conditions. These improved comparison theorems are also considered in the context of a related eigenvalue problem.

Nonexistence of Positive Solutions for Some Fully Nonlinear Elliptic Equations

denote the kth elementary symmetric function, and let Γk denote the connected component of {λ ∈ R : σk(λ) > 0} containing the positive cone {λ ∈ R : λ1 > 0, · · · , λn > 0}. It is well known that Γk = {λ ∈ R : σl(λ) > 0, 1 ≤ l ≤ k}. Let S denote the set of n× n real symmetric matrices. For any A ∈ S we denote by λ(A) the eigenvalues of A. Throughout this note we will assume that Γ ⊂ R is an ope...

Nonexistence of Solutions for Some Nonlinear Elliptic Equations Involving Measures