Results 1 to 10 of about 198 (143)
Demonstratio Mathematica, 2022 By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of
Wang Youyu, Huang Yue, Li Xianfei
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Multi-bump solutions for a Kirchhoff-type problem
Advances in Nonlinear Analysis, 2016 In this paper, we study the existence of solutions for the Kirchhoff problem M(∫ℝ3|∇u|2dx+∫ℝ3(λa(x)+1)u2dx)(-Δu+(λa(x)+1)u)=f(u)$M\Biggl (\int _{\mathbb {R}^{3}}|\nabla u|^{2}\, dx + \int _{\mathbb {R}^{3}} (\lambda a(x)+1)u^{2}\, dx\Biggl ) (- \Delta u +
Alves Claudianor O. +1 more
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Open Mathematics, 2022 In this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u″(t)+(λa+(t)−μa−(t))g(u)=0 ...
Yue Xu, Xiaoling Han
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Maximum principle and its extension for bounded control problems with boundary conditions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 35, Page 1855-1879, 2004., 2004 This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First‐order necessary condition for optimality is obtained in the customary form of the maximum principle, and second‐order necessary condition for optimality of singular controls is derived on the basis of second‐order increment formula ...
Olga Vasilieva
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Nonuniqueness theorem for a singular Cauchy‐Nicoletti problem
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 591-602, 2004., 2004 The problem of nonuniqueness for a singular Cauchy‐Nicoletti boundary value problem is studied. The general nonuniqueness theorem ensuring the existence of two different solutions is given such that the estimating expressions are nonlinear, in general, and depend on suitable Lyapunov functions.
Josef Kalas
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A Simple Expansion‐Based HPM for Cubic–Quintic Damped Nonlinear Oscillator
International Journal of Differential Equations, Volume 2026, Issue 1, 2026.In the present article, a new amplitude expansion–based homotopy perturbation method (AE‐HPM) is used to study the nonlinear behavior of a damped oscillator. The traditional homotopy perturbation method is extended, considering a simple amplitude expansion to determine the solution and amplitude frequency relationship for the damped nonlinear system ...
Nazmul Sharif, Kartik Ariyur
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Nonmonotone impulse effects in second‐order periodic boundary value problems
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 577-590, 2004., 2004 We deal with the nonlinear impulsive periodic boundary value problem u″ = f(t, u, u′), u(ti+) = Ji(u(ti)), u′(ti+) = Mi(u′(ti)), i = 1, 2, …, m, u(0) = u(T), u′(0) = u′(T). We establish the existence results which rely on the presence of a well‐ordered pair (σ1, σ2) of lower/upper functions (σ1 ≤ σ2 on [0, T]) associated with the problem.
Irena Rachůnková, Milan Tvrdý
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.This paper investigates positive solutions for an implicit Caputo fractional boundary value problem of order 0 < ν < 1 on [0, T] with a nonlocal integral boundary condition. By reformulating the problem as an equivalent nonlinear Volterra integral equation, an associated operator on C([0, T], ℝ) is defined, and fixed‐point theory in a cone is employed.
Ngo Ngoc Hung, Youssri Hassan Youssri
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On the discreteness of the spectra of the Dirichlet and Neumann p‐biharmonic problems
Abstract and Applied Analysis, Volume 2004, Issue 9, Page 777-792, 2004., 2004 We are interested in a nonlinear boundary value problem for (|u″|p−2u″)′′=λ|u|p−2u in [0, 1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n − 1
Jiří Benedikt
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This article is devoted to the study of existence, uniqueness, and Ulam–Hyers stability for a coupled system of two nonlinear Caputo‐type multiterm fractional differential equations equipped with coupled closed boundary data. The concept of coupled closed boundary conditions finds its applications in several physical situations, like composite panels ...
Ahmed Alsaedi +3 more
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