We prove the existence of solutions for the following critical Choquard type problem with a
variable-order fractional Laplacian and a variable singular exponent a (-Δ) s (·) u+ b (-Δ) u …

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 …

In this paper, we study the following fractional Schrödinger–Poisson system with
discontinuous nonlinearity: ε 2 s (− Δ) su+ V (x) u+ ϕ u= H (u− β) f (u), in R 3, ε 2 s (− Δ) s ϕ …

In this paper, we consider a class of fractional p‐Laplacian problems with critical and
negative exponents. By decomposition of the Nehari manifold, the existence and multiplicity …

arXiv:2407.20971v1 [math.AP] 30 Jul 2024 Page 1 arXiv:2407.20971v1 [math.AP] 30 Jul 2024
STRONG SOLUTIONS TO SINGULAR DISCONTINUOUS p-LAPLACIAN PROBLEMS …

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 …

We prove the existence of ground state solution to the following problem.\begin {align*}(-
\Delta)^{s} u+ u&=\lambda| u|^{-\gamma-1} u+ P (x)| u|^{p-1} u,~\text {in}~\mathbb {R} …

In this paper, using variational methods, we show the existence of at least two nonnegative
solutions to a class of elliptic problems with fast increasing weights given by-Δ u-1 2 (x·∇ …

In this article, the problem to be studied is the following where Ω is a bounded regular
domain in RN (N≥ 2) containing the origin, p> 1, s∈(0, 1),(N> ps), 0≤ β< 1/c H where c H is …