Related papers: Periodic solutions for some phi-Laplacian and refl…

We study a class of fractional $p$-Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well as characterizations of critical groups and related…

In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the…

We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…

In this paper it is dealt with the following system of difference equations x_{n+1}=((a_{n})/(x_{n}))+((b_{n})/(y_{n})), y_{n+1}=((c_{n})/(x_{n}))+((d_{n})/(y_{n})), n in N_0, where the initial values x_0,y_0 are positive real numbers and…

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An…

We consider initial/boundary value problems for time-fractional parabolic PDE of order $0<\alpha<1$ with Caputo fractional derivative (also called fractional diffusion equations in the literature). We prove well-posedness of corresponding…

In this note, we study the existence and uniqueness of a positive solution to a doubly singular fractional problem with nonregular data. Besides, for some cases, we will show the existence and uniqueness of another notion of a solution,…

This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…

In this paper, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles are investigated. Firstly, we study…

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…

While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori…

We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…

We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.

While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…