The Dirichlet Bvp for the Second Order Nonlinear Ordinary Differential Equation at Resonance
نویسنده
چکیده
Efficient sufficient conditions are established for the solvability of the Dirichlet problem u′′(t) = p(t)u(t) + f(t, u(t)) + h(t) for a ≤ t ≤ b, u(a) = 0, u(b) = 0, where h, p ∈ L([a, b];R) and f ∈ K([a, b];R), in the case where the linear problem u′′(t) = p(t)u(t), u(a) = 0, u(b) = 0 has nontrivial solutions. 2000 Mathematics Subject Classification: 34B15, 34C15, 34C25.
منابع مشابه
Dirichlet series and approximate analytical solutions of MHD flow over a linearly stretching sheet
The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...
متن کاملGeneralized Quasilinearization Method for a Second Order Ordinary Differential Equation with Dirichlet Boundary Conditions
We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.
متن کاملA RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION
Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...
متن کاملAn efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملPositive Solution to a Singular p-Laplacian BVP with Sign-Changing Nonlinearity Involving Derivative on Time Scales
Let T be a time scale such that 0, T ∈ T. By using a monotone iterative method, we present some existence criteria for positive solution of a multiple point general Dirichlet-Robin BVP on time scales with the singular sign-changing nonlinearity. These results are even new for the corresponding differential T R and difference equation T Z as well as in general time scales setting. As an applicat...
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 2007