8 papers · 1 filter
Least energy solutions for a quasilinear Neumann problem
Annamaria Canino, Simone Mauro
We study the existence of nonconstant weak solutions and the qualitative behavior of the least energy level for a class of quasilinear elliptic problems with Neumann boundary condi…
Sobolev Minimizers for Critical Vectorial -Laplacian Problems
Simone Mauro
We study minimizers of the optimal Sobolev quotients for the critical embeddings and $W^{1,p}(Ω;\…
Multiplicity and Regularity Results for Quasilinear Elliptic Systems via Nonsmooth Critical Point Theory
Simone Mauro
We study the quasilinear elliptic system \[ -\textbf{div}(A(x,\boldsymbol u)|D\boldsymbol u|^{p-2}D\boldsymbol u) +\frac{1}{p}\nabla_{\boldsymbol s}A(x,\boldsymbol u)|D\boldsymbol…
On the multiplicity of weak solutions for a class of coupled quasilinear elliptic systems
Annamaria Canino, Simone Mauro
We study the existence and regularity of weak solutions to the following quasilinear elliptic system: \[ -\mathrm{div}(A_k(x, u_k) |\nabla u_k|^{p_k - 2} \nabla u_k) + \dfrac{1}{p_…
Quasilinear Elliptic Cooperative and Competitive Systems
Annamaria Canino, Simone Mauro
We study the existence and multiplicity of weak solutions for the following quasilinear elliptic system: \[ \begin{cases} -\mathrm{div}(A_1(x,u_1)\nabla u_1) + \displaystyle\frac{1…
Quasilinear Equations with Neumann Boundary Conditions
Annamaria Canino, Simone Mauro
We prove a multiplicity result for non-constant weak solutions for the quasilinear elliptic equation \[ \begin{cases} \displaystyle-\text{div}(A(x,u)\nabla u) + \fra…
Existence results for variational quasilinear elliptic systems involving the vectorial -Laplacian
Annamaria Canino, Simone Mauro
We prove existence and regularity results for the following elliptic system: \[ \begin{cases} -\textbf{div}(|D\boldsymbol{u}|^{p-2}D\boldsymbol{u})=\boldsymbol{f}(x,\boldsymbol{u})…
Least Energy Solutions for Cooperative and Competitive Schrödinger Systems with Neumann Boundary Conditions
Simone Mauro, Delia Schiera, Hugo Tavares
We study the following gradient elliptic system with Neumann boundary conditions \begin{equation*} -Δu + λ_1 u = u^3 + βuv^2, \ -Δv + λ_2 v = v^3 + βu^2 v \ \text{in } Ω,\qquad \fr…