Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that [Formula:
see text] admits a positive weak solution in Rn of class D1p (Rn)∩ C1 (Rn∖{0}), whenever …

The goal of this paper is to study the effect of the Hardy potential on the existence and
summability of solutions to a class of nonlocal elliptic problems {(− Δ) su− λ u| x| 2 s= f (x, u) …

Abstract Let 0< s< 1 and p> 1 be such that ps< N. Assume that Ω is a bounded domain
containing the origin. Starting from the ground state inequality by R. Frank and R. Seiringer …

Let Ω⊂ RN be a smooth bounded domain such that 0∈ Ω, N≥ 3. In this paper, we study the
critical quasilinear elliptic problems with Dirichlet boundary condition, where− Δpu=− div (|∇ …

Abstract By the Mountain Pass Theorem and the constrained minimization method existence
of positive or compactly supported radial ground states for quasilinear singular elliptic …

The aim of this paper is to deal with the anisotropic doubly critical equation-Δ p H u-γ [H∘(x)]
pup-1= up∗-1 in RN, where H is in some cases called Finsler norm, H∘ is the dual norm, 1< …

We consider weak positive solutions to the critical p-Laplace equation with Hardy potential
in RN− Δ pu− γ| x| pup− 1= up⁎− 1 where 1< p< N, 0⩽ γ<(N− pp) p and p⁎= N p N− p. The …

Let Ω∋ 0 be an open bounded domain, Ω⊂ RN (N> p2). We are concerned with the
multiplicity of positive solutions of where and Q (x) is a nonnegative function on Ω¯. By …

In this work, we study the following sub-elliptic equations on Carnot group G with Hardy-type
singularity and critical Sobolev–Hardy exponents− Δ G u= λ ψ α| u| 2∗(α)− 2 ud (z) α+ β f (z) …

We study a system of elliptic equations that involves strongly coupled attractive Hardy terms
and critical nonlinearities. The existence of radial decreasing solutions to the system is …