On Unique Solvability of Some Figure-Construction Problems

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

On the Unique Solvability of Some Nonlinear Stochastic Pdes

The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in Hp(T )-space are proved. 1991 Mathematics Subject Classification. 60H15, 35R60.

On Unique Solvability of Boundary Value Problems for Systems of Linear Functional Differential 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...

Solvability for some boundary value problems with φ-Laplacian operators

We study the existence of solution for the one-dimensional φ-laplacian equation (φ(u′))′ = λf(t, u, u′) with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate λ0 is given such that the problem possesses a solution for any |λ| < λ0.