Results 1 to 10 of about 380 (109)
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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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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Asymptotic formulas and critical exponents for two‐parameter nonlinear eigenvalue problems
Abstract and Applied Analysis, Volume 2003, Issue 11, Page 671-684, 2003., 2003 We study the nonlinear two‐parameter problem −u″(x) + λu(x) q = μu(x) p, u(x) > 0, x ∈ (0, 1), u(0) = u(1) = 0. Here, 1 < q < p are constants and λ, μ > 0 are parameters. We establish precise asymptotic formulas with exact second term for variational eigencurve μ(λ) as λ → ∞.
Tetsutaro Shibata
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The main objective of this research involves studying a new novel coupled pantograph system with fractional operators together with nonlocal antiperiodic integral boundary conditions. The system consists of nonlinear pantograph fractional equations which integrate with Caputo fractional operators and Hadamard integrals.
Gunaseelan Mani +4 more
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On boundary value problems for degenerate differential inclusions in Banach spaces
Abstract and Applied Analysis, Volume 2003, Issue 13, Page 769-784, 2003., 2003 We consider the applications of the theory of condensing set‐valued maps, the theory of set‐valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space.
Valeri Obukhovskii, Pietro Zecca
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