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math.AP2026
Elliptic problems involving a diffusion operator of vectorial -Laplacian type
M. L. M. Carvalho, J. R. Santos, H. W. G. Silva
We study a broad class of anisotropic Dirichlet problems driven by the nonhomogeneous operator \[ \mathcal L_Au=-\sum_{i=1}^N\partial_i\!\left( a_i(|\partial_i u|^{p_i})|\partial_i…
math.AP2026
Extremal parameters, multiplicity and nonexistence for a singular elliptic problem
J. C. de Albuquerque, M. L. M. Carvalho, Edcarlos D. Silva +1
We consider the following class of singular elliptic problems \[ \begin{cases} -Δu = -\dfrac{u}{|u|^{β+1}}χ_{\{|u|>0\}} +λ|u|^{p-1}u, & \text{in }Ω,\\[1mm] u=0, & \text{on }\partia…