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Dimensional Reduction for Nonlinear Boundary Value Problems
SIAM Journal on Numerical Analysis, 1988The paper describes a dimension reduction method for a class of strongly nonlinear boundary value problems. The idea is to choose a priori a basis of functions for one of the variables by ways of asymptotic expansions. Numerical experiments are presented.
Jensen, Soren, Babuška, Ivo
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On the solution of a boundary value problem associated with a fractional differential equation
Mathematical methods in the applied sciences, 2020The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order ...
Rezan Sevinik Adıgüzel +3 more
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Multiplicity of Solutions of Nonlinear Boundary Value Problems
SIAM Journal on Mathematical Analysis, 1986The authors consider the one-dimensional Neumann problem \[ (N)\quad u''+g(u)=s+h(t),\quad u'(0)=0=u'(\pi), \] where \(g\in C^ 1(R)\) and g' never vanishes on an interval. Suppose that \(\lim_{u\to - \infty}g'(u)=a,\lim_{u\to +\infty}g'(u)=b,\) where \(b\in ((n-1)^ 2,n^ 2)\) for some integer \(n\geq 1\) and \(h\in C^ 1[0,2\Pi]\). The main result is the
Hart, D. C. +2 more
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Nonlinear Three Point Boundary Value Problem
Sarajevo Journal of MathematicsIn this work, we establish sufficient conditions for the existence of solutions for a three point boundary value problem generated by a third order differential equation. We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. Then by using the Leray Schauder nonlinear alternative we prove the existence of at least
Guezane-Lakoud, Assia, Frioui, A.
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Contraction mappings for nonlinear boundary value problems
Computing, 1968This paper treats mildly nonlinear boundary value problems of the form $$\begin{gathered} y'' (t) + p (t) y'(t) + f(t,y (t)) = 0 \hfill \\ y(\alpha ) = A, y(b) = B \hfill \\ \end{gathered} $$ byPicard-like methods.A priori bounds on a solution are used to ...
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A novel method for nonlinear boundary value problems
Journal of Computational and Applied Mathematics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruimin Zhang, Yingzhen Lin
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On boundary value problems for nonlinear parabolic equations
1957zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Existence Theorem for Nonlinear Boundary Value Problems
Canadian Mathematical Bulletin, 1975Boundary value problems for ordinary differential equations have long been the subject of extensive research activity. In particular, questions concerning the existence and uniqueness of solutions for these problems have received much attention, and algebraic fixed-point theorems have served as important tools in such investigations. For example Picard
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Perturbation Theory of Nonlinear Boundary-Value Problems
Journal of Mathematical Physics, 1969A systematic perturbation theory is presented for the analysis of nonlinear problems. The lowest-order result is just that obtained by linearizing the problem, and the higher-order terms are the solutions of inhomogeneous linear problems. The essential feature of the method is the procedure for avoiding secular terms, which is based on the Lindstedt ...
Millman, M. H., Keller, J. B.
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Expansion Method for Nonlinear Boundary-Value Problems
Journal of Mathematical Physics, 1967A homogeneous nonlinear boundary-value problem, which reduces to the Helmholtz equation when the nonlinearity is removed, is solved by an expansion method using as a basis the eigenfunctions of the linear Helmholtz equation. The nonlinear differential equation is reduced to a nonlinear algebraic system in the expansion coefficients, which can be easily
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