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In the paper, we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problem $x^{Δ} (t) = f (t, x (t))$ , t ∈ T, x(0) = x₀, where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory’s conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result. The results presented...

Existence of solutions to a nonlocal boundary value problem with nonlinear growth.

Lin, Xiaojie (2011)

Boundary Value Problems [electronic only]

Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses.

Chen, Anping, Chen, Yi (2011)

Advances in Difference Equations [electronic only]

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Existence of solutions for a second order abstract functional differential equation with state-dependent delay.

Existence of solutions for fourth-order four-point boundary value problem on time scales.

Existence of solutions for fractional differential inclusions with boundary conditions.

Existence of solutions for $m$ -point boundary value problems on a half-line.

Existence of solutions for nonlinear four-point $p$ -Laplacian boundary value problems on time scales.

Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations.

Existence of solutions for second-order differential equations and systems on infinite intervals.

Existence of solutions for second-order nonlinear impulsive boundary-value problems.

Existence of solutions for some Hammerstein type integro-differential inclusions.

Existence of solutions for some nonlinear beam equations.

Existence of solutions of a functional-integral equation in infinite dimensional Banach spaces

Existence of solutions of a nonlinear system modelling fluid flow in porous media.

Existence of solutions of abstract fractional impulsive semilinear evolution equations.

Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals

Existence of solutions to a nonlocal boundary value problem with nonlinear growth.

Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses.

Existence of solutions to differential inclusions with delayed arguments.

Existence of solutions to fractional order ordinary and delay differential equations and applications.

Existence of solutions to neutral differential equations with deviated argument.

Existence of solutions to nonlinear Langevin equation involving two fractional orders with boundary value conditions.

Currently displaying 81 – 100 of 122