This paper seeks to introduce a new class of fractional Orlicz-Sobolev space with variable-
order. We give basic properties of this space and prove some compactness results. Then …

A short account of some recent existence, multiplicity, and uniqueness results for singular p-
Laplacian problems either in bounded domains or in the whole space is performed, with a …

We classify the non-negative critical points in W 0 1, p (Ω) of J (v)=∫ Ω H (D v)− F (x, v) dx,
where H is convex and positively p-homogeneous, while t↦∂ t F (x, t)/tp− 1 is non …

In this paper, we focus our attention on the singular and nonlocal equation (P)− div (a (x)∇
u)+ η ψ (x)∫ Ω φ u= λ (u+) α+(u+) p in Ω, u= 0 on∂ Ω, for which we prove the existence of …

In this paper we use the dual approach introduced by Colin and Jeanjean (2004) and Liu et
al.(2003) combined with a Rabinowitz's result, Galerkin's method and an approximation …

Existence of solutions to a Φ-Laplacian singular system is obtained via shifting method and
variational methods. A priori estimates are furnished through De Giorgi's technique, Talenti's …

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved.
The equation is driven by the Φ-Laplacian operator, and the reaction term can be …

Existence of solutions to a $\Phi $-Laplacian singular system is obtained via shifting method
and variational methods. A priori estimates are furnished through De Giorgi's technique …

It is established existence and multiplicity of solution for the following class of quasilinear
elliptic problems $$\left\{\begin {array}{lr}-\Delta_\Phi u=\lambda a (x)| u|^{q-2} u+| u|^{p-2} u …

In this paper, we consider a class of nonlocal problem with strong singularity and sublinear
term in the nonlinearity. The nonlocal term may change sign. Combining the variational …