ﻻ يوجد ملخص باللغة العربية
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.
We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $pge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $Omega$. By means of barriers, a nonlocal superposition pri
We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibit partial symmetry. Furthermore, we show that Semi
We consider a nonlinear pseudo-differential equation driven by the fractional $p$-Laplacian $(-Delta)^s_p$ with $sin(0,1)$ and $pge 2$ (degenerate case), under Dirichlet type conditions in a smooth domain $Omega$. We prove that local minimizers of th
We propose two asymptotic expansions of the two interrelated integral-type averages, in the context of the fractional $infty$-Laplacian $Delta_infty^s$ for $sin (frac{1}{2},1)$. This operator has been introduced and first studied in [Bjorland-Caffare
We investigate the existence of infinitely many radially symmetric solutions to the following problem $$(-Delta_p)^s u=g(u) textrm{ in } mathbb{R}^N, uin W^{s,p}(mathbb{R}^N),$$ where $sin (0,1)$, $2 leq p < infty$, $sp leq N $, $2 leq N in mat