The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities:\begin{equation*}\left\{\begin{array}{ll} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1 }\quad \text{in }\Omega,\\ u>0,\;\;\;\;\quad u=0,\;\;\;\;\quad }\mathbb{R}^{N}\setminus \Omega,\end{array} \right. \end{equation*} where $\Omega$ bounded domain ...

<p style='text-indent:20px;'>This paper is concerned with the nonlocal dispersal equations inhomogeneous bistable nonlinearity in one dimension. The varying consists of two spatially independent nonlinearities, which are connected by a compact transition region. We establish existence unique entire solution connecting traveling wave solutions pertaining to different nonlinearities. In par...

In this paper, we study the following nonlocal problem − open="(" close=")"> a b ∫ Ω open="|" close="|"> ∇ u 2 <...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

We address ring-shaped surface waves supported by defocusing thermal media with circular cross-section. Such waves exist because of the balance between repulsion from the interface and deflection of light from the bulk medium due to defocusing nonlocal nonlinearity. The properties of such surface waves are determined by the geometry of the sample. Nodeless ring surface waves are stable for all ...