Flows and Critical Points

Abstract

Abstract.We use flows and the cohomological index to adapt the method of sandwich pairs to better suit quasilinear elliptic boundary value problems. Mathematics Subject Classification (2000). Primary 35J65, Secondary 47J10, 47J30.

Fractional p-Laplacian Equations with Sandwich Pairs

“…Once we obtain the particular cases, i.e., the problems ( 28)- (30), the results investigated here, Theorems 1 and 2, are valid for such a case. It is possible to notice that the freedom of choice of the function ψ(•) allows obtaining other examples involving fractional operators; however, we restrict ourselves to the ones previously discussed.…”

“…This approach was taken by Schechter [28]. We can also highlight the works on solved quasilinear problems using cones as sandwich pairs [29,30]. See the works in [31][32][33].…”

“…The sandwich pairs used until 2007 were introduced using the eigenspaces of a semilinear operator and are therefore unsuitable for dealing with quasilinear problems where there are no eigenspaces. In this sense, in 2008, Perera and Scheter [30], showed that the method could be modified to be applied in the problem (2).…”

“…Motivated by these works [29,30,38], in this paper we tried to find a solution to the problem (1) via variational methods and sandwich pairs. We will discuss the existence of solutions through two theorems, one with the lower limit condition, and the other with the upper limit condition and from the function…”

Sandwich pairs for p-Laplacian systems

“…In [6] sandwich pairs constructed using the eigenspaces of a linear operator were used to solve semilinear elliptic boundary value problems, and in [4,5] the authors solved quasilinear problems using cones as sandwich pairs. In the present paper we use more general curved sandwich pairs made up of orbits of a certain group action on product spaces to solve systems of quasilinear equations.…”