[PDF] Top 20 On a fractional differential equation with infinitely many solutions

... In the last number of years, it became evident that differential equations of non-integer order, also called fractionals (FDE’s), can capture better in models many of the relevant features of complex phenomena from ... See full document

... We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the p-Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part, even under small ... See full document

... We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the ... See full document

... of infinitely many solutions of P, under the assumption that V x is a function possibly changing sign in R N and fx, u also satisfies some growth ... See full document

... are many papers on the existence of periodic solutions for p-Laplacian elliptic systems, for example 21–24 ...periodic solutions for variable exponent systems are ...of infinitely many ... See full document

... periodic solutions for ordinary p(t)-Laplacian system under the generalized Ambrosetti-Rabino- witz ...of infinitely many large energy solutions and small energy ...of infinitely ... See full document

... the p-Laplacian, p ∗ = pN /(N – p) is the critical Sobolev exponent and λ >  is a parameter. The first existence result of Problem (.) with p =  was obtained by Brezis and Nirenberg in the celebrated paper []. In ... See full document

... Furthermore, the p-Laplacian often occurs in non-Newtonian fluid theory, nonlinear elastic mechanics, and so on. So, the impulsive fractional boundary value problem with p- Laplacian is worth considering. For ... See full document

... the equation in (10) is a fuzzy algebraic equation and its solution can be determined by applying usual algebraic operations taking care about the arithmetic of fuzzy numbers (see ...of equation (10) ... See full document

... where s ∈ (0, 1) is fixed, N > 2s, V : R N → R + is an electric potential, the magnetic potential A : R N → R N is a continuous function, and (–) s A is the fractional magnetic operator. Under suitable ... See full document

... the fractional Schrödinger equation (– ) α u + V(x)u = f (x,u), x ∈ R N , where 0 < α < 1, N > 2 α , (– ) α stands for the fractional Laplacian of order α , V is a positive continuous ... See full document

... in many areas, including fluid flow, electrical net- works, probability and statistics, chemical physics and signal processing and so on; see [–] and the references ...been many papers dealing with the ... See full document

... infinitely many solutions of this problem when the nonsmooth potentials F have suitable oscillating behavior in any neighborhood of the origin (respectively the infinity) and discuss the properties of the ... See full document

... Remark 1.1 In [2,3], they got sign-changing solutions for elliptic problem with Dirichlet boundary value. Those abstract results involved a Banach space of continuous functions in the Hilbert space, where the cone ... See full document

... 39] similar methods were used to study various Schrödinger equations with perturbations. Motivated by the above papers, in this paper we use variant fountain theorems to study the existence of nontrivial solutions ... See full document

... 7. Oyedepo T, Taiwo OA, Abubakar JU, Ogunwobi ZO (2016) “Numerical Studies for Solving Fractional Integro-Differential Equations by using Least Squares Method and Bernstein Polynomials”. Fluid Mech Open Acc ... See full document

... Motivated by the above works, in the present paper we study the existence of infinitely many solutions for problem (.) when the nonlinear term f (x, u) satisfies the superlinear condition and sublinear ... See full document

... Schrödinger equation (1.3), but for fractional Schrödinger equation of the form ...in fractional Sobolev spaces, especially when the potential function V (x) van- ishes at ...the ... See full document

... of equation furnishes a model for studying traveling wave in suspension bridges (see ...arguments, many authors investigated nonlinear biharmonic equations under Dirichlet boundary conditions or Navier ... See full document

... of fractional calculus and fractional ordinary and partial dif- ferential equations recently; for instance see ...[–]. Many researchers have explored the existence of solutions for ... See full document