Here, a singular boundary value problem involving the (p, q)-Laplacian operator in a smooth bounded domain in R N is considered. Using the variational method and critical point theory, the existence of two weak solutions is proved.

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.

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