Main objective of this paper is to study positive decaying solutions for a class of quasilinear problems with weights. We consider one dimensional problems on an interval which may be finite or infinite. In particular, when the interval is infinite, unlike the known cases in&#...

We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on the exterior of a bounded domain. We prove the existence of positive weak solution for classes of sublinear nonlinearities including logistic type. A method of sub- and super...

A dessin is a 2-cell embedding of a connected 2-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of orientation- and colour-preserving automorphisms acts regularly on the edges. In this paper we study regular dessins whose underlying grap...

The paper gives a global decomposition theorem for edge‐colorings of complete bipartite graphs without properly colored C4. As a corollary, a result on the existence of a monochromatic star is obtained.

We consider a nonlocal problem with the fractional Laplacian operator on a bounded domain with smooth boundary and depending on a bifurcation parameter near resonance at the principal eigenvalue. The nonlinear perturbation is sublinear at infinity. We use bifurcation theory to establish ...