Abstract In this paper, we study the existence of non-negative non-trivial solutions for a class double-phase problems where source term is Caratheodory function that satisfies Ambrosetti–Rabinowitz type condition in framework Sobolev–Orlicz spaces with variable exponents complete manifold. Our approach based on Nehari manifold and some variational techniques. Furthermore, Hölder ine-quality, c...

Sequences of entropy solutions of a non-degenerate first-order quasilinear equation are shown to be strongly pre-compact in the general case of a Caratheodory flux vector. Existence of the weak and entropy solution to Cauchy problem for such equation is also established. The proofs are based on general localization principle for H-measures corresponding to sequences of measure-valued functions....

and Applied Analysis 3 3. Main Results Throughout this paper, we will consider lattices as complete lattices,X will denote space, and μ is a membership function of any fuzzy set X. Definition 3.1. If m : σ L → R ∪ {∞} satisfies the following properties, then m is called a lattice measure on the lattice σ-algebra σ L . i m ∅ L0. ii For all f, g ∈ σ L such that m f , m g ≥ L0 : f ≤ g ⇒ m f ≤ m g ...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

In this paper, we study a class of fractional q-differential inclusion order 0 &lt; q 1 under L1-Caratheodory with convex-compact valued properties on multifunctions. By the use existence fixed point for closed contractive multifunction complete metric space which has been proved by Covitz and Nadler, provide solutions problem via some conditions. Also, give couple examples to elaborate our resul...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.