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On W1,p estimates for elliptic equations in divergence form
First, we will apply the method to study W 1,p regularity for a nonlinear elliptic operator in divergence form. We would like to point out that in the particular case of a linear elliptic equation,…
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Multiplicity Results for Some Nonlinear Elliptic Equations
Abstract This paper deals with the existence of multiple solutions for some classes of nonlinear elliptic Dirichlet boundary value problems. The interplay of convex and concave nonlinearities is…
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A convex-concave problem with a nonlinear boundary condition
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Perturbation of Δu+u(N+2)/(N−2)=0, the Scalar Curvature Problem in RN, and Related Topics
Abstract Some nonlinear elliptic equations on R N which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature…
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Existence and nonexistence results for quasilinear elliptic equations involving the p-laplacian
The paper deals with the study of a quasilinear elliptic equation involving the p-laplacian with a Hardy-type singular potential and a critical nonlinearity. Existence and nonexistence results are…
Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential
We prove existence, qualitative properties and asymptotic behavior of positive solutions to the doubly critical problem $$\begin{aligned} (-\Delta )^s u=\vartheta \frac{u}{|x|^{2s}}+u^{2_s^*-1},…
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Some results for semilinear elliptic equations with critical potential
This paper is devoted to the study of the elliptic problems with a critical potential, where N ≥ 3, λ ≥ 0 and 0 < q < 1 < p ≤ (N + 2)/(N − 2). Existence, multiplicity, behaviour in x = 0 and…
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Some remarks on the solvability of non-local elliptic problems with the Hardy potential
The aim of this paper is to study the solvability of the following problem, where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded…
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Some improved Caffarelli-Kohn-Nirenberg inequalities
Abstract.For 1 < p < N and $-\infty < \gamma < \frac{N-p}{p}$ we obtain the following improved Hardy-Sobolev Inequalities$$ \int\limits_\Omega \vert\nabla \phi\vert^p\vert x\vert^{-p\gamma}dx…
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Existence and nonexistence results for quasilinear elliptic equations involving the p-Laplacian with a critical potential
This paper deals with the existence and nonexistence results for quasilinear elliptic equations of the form -Δpu=f(x, u), where Δp:=div(|∇u|p-2∇u), p>1, and the solutions are understood in the sense…
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