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In this paper, we obtain necessary and sufficient conditions for the oscillation of solutions to a second-order neutral differential equation with impulses. Two examples are provided to show the effectiveness and feasibility of the main results. Our main tool is Lebesgue's dominated convergence theorem. [ABSTRACT FROM AUTHOR]

In this paper, we study oscillatory properties of neutral differential equations. Moreover, we discuss some examples that show the effectiveness and the feasibility of the main results. [ABSTRACT FROM AUTHOR]

In this work, we obtain necessary and sufficient conditions for the oscillation of the solutions to a second-order neutral differential equation with mixed delays. Two examples are provided to show effectiveness and feasibility of main results. Our main tool is the Lebesgue's Dominated Convergence theorem. [ABSTRACT FROM AUTHOR]

We consider a Dirichlet problem driven by a (p(z), q(z))-Laplacian and a reaction involving the sum of a parametric singular term plus a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter λ > 0 varies. Also we show that for every admissible parameter the problem has a smallest positive solution and obtain the monotonicity and continuity properties of the minimal solution map. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional p (⋅) -Laplacian with concave–convex nonlinearities when, in general, the nonlinear term does not satisfy the Ambrosetti–Rabinowitz condition. The main tools for obtaining this result are the mountain pass theorem and a modified version of Ekeland's variational principle for an energy functional with the compactness condition of the Palais–Smale type, namely the Cerami condition. Also we discuss several existence results of a sequence of infinitely many solutions to our problem. To achieve these results, we employ the fountain theorem and the dual fountain theorem as main tools. [ABSTRACT FROM AUTHOR]

We consider a Robin problem driven by the (p, q)-Laplacian plus an indefinite potential term. The reaction is either resonant with respect to the principal eigenvalue or (p - 1) -superlinear but without satisfying the Ambrosetti-Rabinowitz condition. For both cases we show that the problem has at least five nontrivial smooth solutions ordered and with sign information. When q = 2 (a (p, 2)-equation), we show that we can slightly improve the conclusions of the two multiplicity theorems. [ABSTRACT FROM AUTHOR]

We obtain a modified version of the Spanne–Peetre inequality in the context of Morrey spaces with mixed norm. The geometric structure of the mixed Morrey spaces under consideration, dictates the new definition of Morrey–Lipschitz space. The Spanne–Peetre inequality that we find ensures that if a function belongs to a suitable Morrey space with mixed norm, then the modified integral operator which characterizes the Spanne–Peetre inequality, belongs to a suitable Morrey–Lipschitz space. [ABSTRACT FROM AUTHOR]

We consider a nonlinear elliptic Dirichlet problem driven by the anisotropic (p, q)-Laplacian and with a reaction which is nonparametric and has the combined effects of a singular and of a superlinear terms. Using variational tools together with truncation and comparison techniques, we show that the problem has at least two positive smooth solutions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show some regularity properties of solutions to Lu=f, where L is a second order nondivergence form operator and f belongs to a homogeneous Herz space K˙q(⋅)α,p(⋅) with two variable exponents. [ABSTRACT FROM AUTHOR]