On the index instability for some nonlocal elliptic problems

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...

Nonlocal Elliptic Boundary Value Problems

On Some Elliptic Problems with Nonlocal Boundary Coefficient-operator Conditions in the Framework of Hölderian Spaces

In this paper we give some new results on second order differentialoperator equations of elliptic type with nonregular boundary conditions with coefficient-operator. The study is developped in Hölder spaces and uses the reduction method of S. G. Krein. Necessary and sufficient conditions of compatibility are established to obtain different types of solutions. Maximal regularity properties are a...

Generalized Solutions of Nonlocal Elliptic Problems

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

Existence, Uniqueness and Multiplicity of Positive Solutions for Some Nonlocal Singular Elliptic Problems

In this article, using the sub-supersolution method and Rabinowitztype global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.