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In this note, we present some criteria for the oscillation of second-order neutral delay differential equations. Precisely, we state a result related to the oscillation of unbounded solutions of the equation under consideration and a result related to the oscillation and the convergence for every solution of the same equation. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence of a second-order Lagrangian for a fourth-order ordinary differential equation. Our approach is based on the Fels' conditions. [ABSTRACT FROM AUTHOR]

In this note we show some results dealing with solutions of constant sign and nodal solutions to nonlinear Robin problems with sign-changing potential and jumping reaction term. [ABSTRACT FROM AUTHOR]

In this note we present a regularity result for solutions of parabolic equations in the framework of mixed Morrey spaces. In order to study the regularity properties, we use the representation formula for the solutions of the differential equations under consideration and we need of boundedness results for integral operators and commutators. [ABSTRACT FROM AUTHOR]

In this note we study the behaviour of Hardy-Littlewood Maximal Operator and we obtain an estimate for commutators on Generalized Local Morrey Spaces. These results can be applied in the study of regularity of solutions of elliptic partial differential equations with discontinuous coefficients. [ABSTRACT FROM AUTHOR]

Aim of this study is to obtain an interior estimate for the solution of the Dirichlet problem for a linear elliptic partial di erential equations having the coefficients of the principal part that belong to the Sarason class VMO of functions with vanishing mean oscillation. In order to obtain the desidered result we use some estimates for singular integral operators and commutators on Generalized Local Morrey Spaces. [ABSTRACT FROM AUTHOR]