Singular Differential, Integral and Discrete Equations: the Semipositone Case
نویسندگان
چکیده
Fixed point methods play a major role in the paper. In particular, we use lower type inequalities together with Krasnoselskii’s fixed point theorem in a cone to deduce the existence of positive solutions for a general class of problems. Moreover, the results and technique are applicable also to positone problems. 2000 Math. Subj. Class. 34B15, 47H30, 39A10.
منابع مشابه
Solving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملFinite difference method for solving partial integro-differential equations
In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...
متن کاملPositive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations
In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations Du(t) + λf(t, u(t), v(t)) = 0, Dv(t) + λg(t, u(t), v(t)) = 0, t ∈ (1, e), λ > 0, u(1) = v(1) = 0, 0 ≤ j ≤ n− 2, u(e) = μ ∫ e 1 v(s) ds s , v(e) = ν ∫ e
متن کاملConvergence analysis of product integration method for nonlinear weakly singular Volterra-Fredholm integral equations
In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...
متن کاملNumerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
Introduction Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic integral equations. Weakly singular integral equation is one of the principle type of integral equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002