We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to ...

We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking ideal is S1, in Hrushovski’s terminology). Using it we prove an independence theorem over extension bases (whic...

Keywords: Positive solutions Third-order three-point BVPs Nonhomogeneous Fixed point theorem Existence and nonexistence a b s t r a c t In this work, by employing the Guo–Krasnosel'skii fixed point theorem and Schauder's fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary value problem u (t) + a(t)f (u(t)) = 0...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Abstract In this paper, the existence of solutions for differential inclusions of fractional order q ∈ (1, 2] with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not ...

This paper investigates the existence of positive solutions for a sixth-order m-point boundary value problem with three variable parameters. Many problems in the theory of elastic stability can be handled by the method of multi-point problems. By using the fixed point theorem and operator spectral theorem, we give a new existence result.

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

In this paper, we first establish decay estimates for the fractional and higher-order H\'enon-Lane-Emden systems by using a nonlocal average integral estimates, which deduce result of non-existence. Next, apply method scaling spheres introduced in \cite{DQ2} to derive Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).

In this paper, we establish some existence results for higher-order nonlinear fractional differential inclusions with multi-strip conditions, when the right-hand side is convex-compact as well nonconvexcompact values. First, use alternative of Leray-Schauder type multivalued maps. We investigate next result by using well-known Covitz and Nadler?s fixed point theorem contractions. The are illust...

Abstract In this article, our aim is to establish a generalized version of Lions-type theorem for the p -Laplacian. As an application theorem, we consider existence ground state solution quasilinear elliptic equation with critical growth.