Results 11 to 20 of about 125 (84)
Three‐Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three‐point boundary conditions by means of standard tools of the fixed‐point theorems for single and multivalued functions.
Athasit Wongcharoen +4 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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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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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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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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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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Multiplicity results for asymmetric boundary value problems with indefinite weights
Abstract and Applied Analysis, Volume 2004, Issue 11, Page 957-979, 2004., 2004 We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u″ + f(t, u) = 0, u(0) = u(T) = 0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights.
Francesca Dalbono
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Bounded solutions of Carathéodory differential inclusions: a bound sets approach
Abstract and Applied Analysis, Volume 2003, Issue 9, Page 547-571, 2003., 2003 A bound sets technique is developed for Floquet problems of Carathéodory differential inclusions. It relies on the construction of either continuous or locally ipschitzian Lyapunov‐like bounding functions. Proceeding sequentially, the existence of bounded trajectories is then obtained. Nontrivial examples are supplied to illustrate our approach.
Jan Andres +2 more
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A Higher Order Nonresonant p-Laplacian Boundary Value Problem on an Unbounded Domain
Abstract and Applied AnalysisMSC2010 Classification: 34B10 ...
S. A. Iyase, O. F. Imaga
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