Solutions to conjectures on a nonlinear recursive equation

Özkan Öcalan; Oktay Duman

Displaying similar documents to “Solutions to conjectures on a nonlinear recursive equation”

Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term

Mama Abdelli, Abderrahmane Beniani, Nadia Mezouar, Ahmed Chahtou (2023)

Mathematica Bohemica

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We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t \to \infty$ by applying the Lyapunov method.

Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1

Mami Suzuki (2011)

Annales Polonici Mathematici

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For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where $X (x, y) = λ ₁ x + μ y + \sum_{i + j \geq 2} c_{i j} x^{i} y^{j}$ , $Y (x, y) = λ ₂ y + \sum_{i + j \geq 2} d_{i j} x^{i} y^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂|...

Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane

Eugenia N. Petropoulou, Panayiotis D. Siafarikas (2000)

Archivum Mathematicum

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An existence and uniqueness theorem for solutions in the Banach space $l_{1}$ of a nonlinear difference equation is given. The constructive character of the proof of the theorem predicts local asymptotic stability and gives information about the size of the region of attraction near equilibrium points.

Multiplicity of positive solutions for a nonlinear fourth order equation

D. R. Dunninger (2001)

Annales Polonici Mathematici

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We study the existence and multiplicity of positive solutions of the nonlinear fourth order problem ⎧ $u^{(4)} = λ f (u)$ in (0,1), ⎨ ⎩u(0) = a ≥ 0, u’(0) = a’ ≥ 0, u(1) = b ≥ 0, u(1) = -b’ ≤ 0 The methods employed are upper and lower solutions and degree theory arguments.

On the system of two nonlinear difference equations $x_{n + 1} = A + x_{n - 1} / y_{n}, y_{n + 1} = A + y_{n - 1} / x_{n}$ .

Papaschinopoulos, G., Schinas, C.J. (2000)

International Journal of Mathematics and Mathematical Sciences

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Positive solutions to a class of elastic beam equations with semipositone nonlinearity

Qingliu Yao (2010)

Annales Polonici Mathematici

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Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem $u^{(4)} (t) = f (t, u (t), u^{'} (t))$ , 0 < t < 1, u(0) = u’(0) = u’(1) =u”’(1) =0, where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the...

Strong $94_{2}^{0}$ categoricity.

С.Дж. Аш, С.С. Гончаров, S.S. Gončarov, S.S. Gončarov (1985)

Algebra i Logika

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Existence of positive solutions for a nonlinear fourth order boundary value problem

Ruyun Ma (2003)

Annales Polonici Mathematici

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We study the existence of positive solutions of the nonlinear fourth order problem $u^{(4)} (x) = λ a (x) f (u (x))$ , u(0) = u’(0) = u”(1) = u”’(1) = 0, where a: [0,1] → ℝ may change sign, f(0) < 0, and λ < 0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.

Some results on strongly nonlinear anisotropic differential equations

L. Bougoffa, A. El Khalil, S. El Manouni (2010)

Applicationes Mathematicae

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The paper concerns the existence of weak solutions to nonlinear elliptic equations of the form A(u) + g(x,u,∇u) = f, where A is an operator from an appropriate anisotropic function space to its dual and the right hand side term is in $L^{1 + m}$ with 0 < m < 1. We assume a sign condition on the nonlinear term g, but no growth restrictions on u.

Stability and boundedness of solutions of nonlinear vector differential equations of third order

Mathew Omonigho Omeike (2014)

Archivum Mathematicum

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The paper studies the equation $\overset{⃛}{X} + Ψ (\dot{X}) \ddot{X} + Φ (X) \dot{X} + c X = P (t)$ in two cases: (i) $P (t) \equiv 0$ , (ii) $P (t) \neq 0$ . In case (i), the global asymptotic stability of the solution $X = 0$ is studied; in case (ii), the boundedness of all solutions is proved.

Some Remarks on Nonlinear Composition Operators in Spaces of Differentiable Functions

J. Appell, Z. Jesús, O. Mejía (2011)

Bollettino dell'Unione Matematica Italiana

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In this note we study the nonlinear composition operator $f\mapsto g\circ f$ in various spaces of differentiable functions over an interval. It turns out that this operator is always bounded in the corresponding norm, whenever it maps such a space into itself, but continuous only in exceptional cases.