Existence of a mountain pass solution for a nonlocal fractional $(p, q)$-Laplacian problem

Abstract

Here, a nonlocal nonlinear operator known as the fractional $(p,q)$ ( p , q ) -Laplacian is considered. The existence of a mountain pass solution is proved via critical point theory and variational methods. To this aim, the well-known theorem on the construction of the critical set of functionals with a weak compactness condition is applied.

Negative Energy Solutions for a New Fractionalpx-Kirchhoff Problem without the (AR) Condition

“…In the past few decades, many people studied the fractional p-Laplace operator problem, and we refer the readers to [1][2][3][4][5][6][7][8][9]. We point out that Behboudi et al studied the existence of mountain pass solution for the nonlocal fractional ðp, qÞ-Laplacian problem in [10] by using the variational method. The more general problem is the following pðxÞ-Laplacian equation…”

A weak solution for a $(p(x),q(x))$-Laplacian elliptic problem with a singular term

“…The differential operator p + q is known as the (p, q)-Laplacian operator, if p = q, where j , j > 1 denotes the j-Laplacian defined by j u := div(|∇u| j-2 ∇u). It is not homogeneous, thus some technical difficulties arise in applying the usual methods of the theory of elliptic equations (for further details, see [1,2,5,7,8,10,[12][13][14][15][16][19][20][21][22][23] and references therein).…”

A nonlinear fractional Rayleigh–Stokes equation under nonlocal integral conditions

“…Moreover, there has currently been a considerable increase in examining fractional partial differential equations (FPDEs). We can list several current remarkable research studies; for instance, Abdolrazaghi and Razani [3], Behboudi et al [4], Ding and Neito [5], Agarwal et al [6], Baleanu [7], Adiguzel et al [8][9][10], Afshari et al [11], Alqahtani et al [12], Karapinar et al [13], Abdeljawad et al [14], Baitiche et al [15], Ardjouni [16] and the references therein.…”