The aim of this paper is twofold. On one hand we establish a three critical points theorem for functionals depending on a real parameter λ ∈ Λ, which is different from the one proved by B. Ricceri in [15] and gives an estimate of where Λ can be located. On the other hand, as an application of the previous result, we prove an existence theorem of three classical solutions for a two-point boundar...

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole RN .

and Applied Analysis 3 ii If γ n − 1 and f ∈ ACn−1 a, b ,R , then CaD t f t and t Dn−1 b f t are represented by C aD n−1 t f t f n−1 t , t D n−1 b f t −1 n−1 f n−1 t , t ∈ a, b . 2.3 With these definitions, we have the rule for fractional integration by parts, and the composition of the Riemann-Liouville fractional integration operator with the Caputo fractional differentiation operator, which ...

In this paper, we study a Neumann problem for elliptic systems with variable exponents and we obtain the existence of at least three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem [12].