منابع مشابه
Some remarks on singular solutions of nonlinear elliptic equations. I
We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes. Mathematics Subject Classification (2000). 35J69, 58J05, 53C21, 35J60.
متن کاملSolving 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 کاملOn the Nonexistence of Positive Solution of Some Singular Nonlinear Integral Equations
We consider the singular nonlinear integral equation u(x)= ∫RN g(x, y,u(y))dy/|y− x|σ for all x ∈ RN , where σ is a given positive constant and the given function g(x, y,u) is continuous and g(x, y,u) ≥M|x|β1|y|β(1 + |x|)−γ1 (1 + |y|)−γuα for all x, y ∈ RN , u ≥ 0, with some constants α,β,β1,γ,γ1 ≥ 0 and M > 0. We prove in an elementary way that if 0 ≤ α ≤ (N + β− γ)/(σ + γ1 − β1), (1/2)(N + β ...
متن کاملOn Monotonic Solutions of Some Integral Equations
Integral equations arise naturally in applications of real world problems [5, 6, 7, 8]. The theory of integral equations has been well developed with the help of various tools from functional analysis, topology and fixed-point theory. The classical theory of integral equations can be generalized if one uses the Stieltjes integral with kernels dependent on one or two variables. The aim of this p...
متن کاملSolutions for Singular Volterra Integral Equations
0 gi(t, s)[Pi(s, u1(s), u2(s), · · · , un(s)) + Qi(s, u1(s), u2(s), · · · , un(s))]ds, t ∈ [0, T ], 1 ≤ i ≤ n where T > 0 is fixed and the nonlinearities Pi(t, u1, u2, · · · , un) can be singular at t = 0 and uj = 0 where j ∈ {1, 2, · · · , n}. Criteria are offered for the existence of fixed-sign solutions (u∗1, u ∗ 2, · · · , u ∗ n) to the system of Volterra integral equations, i.e., θiu ∗ i (...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1964
ISSN: 0386-2194
DOI: 10.3792/pja/1195522745