Functional fractional boundary value problems with singular -Laplacian

Periodic solutions for some phi-Laplacian and reflection equations

“…G is positive on non-zero values, so equation (9) implies that, F(x(t)) < G(g(c 2 )) + F(c 1 ) for all t ∈ (a,t 0 ).…”

“…The φ -Laplacian is studied from different points of view in several papers, e. g. [1,9,13,21,23,25,26]. Actually, if we consider the problem with the f −1 -Laplacian…”

Fractional BVPs with strong time singularities and the limit properties of their solutions

“…(⇒) Let be a solution of (3), (4). Then equality (10) holds, where ∈ R. We now imply I α to both sides of (10) and have, by Lemma 2.3,…”

“…Section 2 contains the results from the fractional calculus and the technical lemmas that are used in the next sections. In Section 3, an operator is introduced and it is shown that is a solution of (3), (4) if and only is a fixed point of . The proofs of Theorem 1.1, Corollary 1.2 and an example are given in Section 4.…”

Multiplicity of solutions for mean curvature operators with minimum and maximum in Minkowski space

“…Note that φ : R → R is an odd increasing homeomorphism; the classical p-Laplacian cases, for which φ(s) = |s| p-2 s, the existence and multiplicity results of p-Laplacian problem with functional boundary conditions have been studied in [18,20] and [22]; for the other cases, see [21]. Also, functional fractional boundary value problems with a singular φ-Laplacian were studied in [11].…”