# Existence of solutions for a class of nonlinear boundary value problems on half-line

2012-4-16
Ertem, Türker
Zafer, Ağacık
Consider the infinite interval nonlinear boundary value problem (p(t)x ) + q(t)x = f (t, x), t ≥ t0 ≥ 0, x(t0) = x0, x(t) = a v(t) + b u(t) + o(ri(t)), t → ∞, where u and v are principal and nonprincipal solutions of (p(t)x’)’ + q(t)x = 0, r1(t) = o (u(t)(v(t))μ ) and r2(t) = o(v(t)(u(t))μ ) for some μ Î (0, 1), and a and b are arbitrary but fixed real numbers. Sufficient conditions are given for the existence of a unique solution of the above problem for i = 1, 2. An example is given to illustrate one of the main results.
Boundary Value Problems

# Suggestions

 Application of a Robust Multigrid Technique for the Parallel Solution of Initial-Boundary Value Problems Martynenko, S.I.; Gökalp, İskender; Bakhtin, V.A.; Karaca, Mehmet; Toktaliev, P.D.; Semenev, P.A. (2022-12-01) This article is devoted to the construction of a parallel multigrid algorithm for the numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on a robust multigrid technique (RMT). A distinctive feature of the proposed algorithm is the possibility of the parallel solution of initial-boundary value problems and initial-boundary value problems in a unified manner involving 3m independent computers (threads, if the OpenMP parallelization technology is used), m = 1, 2, 3, …. C...
 A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind Kaya, Ruşen; Taşeli, Hasan (2022-01-01) A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
 REGULARITY OF QUOTIENTS OF DRINFELD MODULAR SCHEMES Kondo, Satoshi; Yasuda, Seidai (Mathematical Sciences Publishers, 2020-02-01) Let A be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal I subset of A, Drinfeld defined the notion of structure of level I on a Drinfeld module.
 Value sets of bivariate Chebyshev maps over finite fields Küçüksakallı, Ömer (2015-11-01) We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.
 Joint densities of hitting times for finite state Markov processes Bielecki, Tomasz R.; Jeanblanc, Monique; Sezer, Ali Devin (2018-01-01) For a finite state Markov process X and a finite collection {Gammak, k is an element of K} of subsets of its state space, let tauk be the first time the process visits the set Gammak. In general, X may enter some of the Gammak at the same time and therefore the vector tau := (tauk, k is an element of K) may put nonzero mass over lower dimensional regions of R+ vertical bar K vertical bar;these regions are of the form Rs ...
Citation Formats
T. Ertem and A. Zafer, “Existence of solutions for a class of nonlinear boundary value problems on half-line,” Boundary Value Problems, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51230.