Nonlinear Second Order Elliptic Partial Differential Equations at Resonance

Perturbing Fully Nonlinear Second Order Elliptic Equations

We present two types of perturbations with reverse effects on some scalar fully nonlinear second order elliptic differential operators: on the other hand, first order perturbations which destroy the global solvability of the Dirichlet problem, in smooth bounded domains of Rn; on the other hand, an integral perturbation which restore the local solvability, on compact connected manifolds without ...

Second-order Differential Equations and Nonlinear Connections

The main purposes of this article are to extend our previous results on homogeneous sprays [15] to arbitrary secondorder differential equations, to show that locally diffeomorphic exponential maps can be defined for any of them, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. In the process, we introduce vertically homogeneous connections. Unlike...

Second Order Linear and Nonlinear Differential Equations'

Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [Z. Cai et al., SIAM J. Numer. Anal., 39 (2001), pp. 1418–1445], in order to retain the full efficiency of the L2 norm first-order system leastsquares (FOSLS) approach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach of...

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...