Presents a Morse theoretic study of a very general class of homogeneous operators that
includes the $ p $-Laplacian as a special case. The $ p $-Laplacian operator is a …

We study the zero Dirichlet problem for the equation− Δ pu− Δ qu= α| u| p− 2 u+ β| u| q− 2 u
in a bounded domain Ω⊂ ℝ N, with 1< q< p. We investigate the relation between two critical …

We construct a positive solution to a quasilinear parabolic problem in a bounded spatial
domain with the p-Laplacian and a nonsmooth reaction function. We obtain nonuniqueness …

We consider a parabolic-elliptic system of partial differential equations with a chemotactic
term in a N-dimensional unit ball “B” describing the behavior of a biological species “u” and …

Abstract We prove the Strong Maximum Principle (SMP) under suitable assumptions for a
class of quasilinear parabolic problems with the p-Laplacian, p> 1, on bounded cylindrical …

We investigate strong and weak versions of maximum and comparison principles for a class
of quasilinear parabolic equations with the p-Laplacian ∂ _t u-Δ _p u= λ| u|^ p-2 u+ f (x, t)∂ …

In this article, the main objective is to prove the existence of non-radial nodal (sign-
changing) solutions of the above problem (P), in the case where the exponent a is the critical …

In this paper we provide a comparison principle for the weak solutions u (⋅, t), v (⋅, t) u (·, t),
v (·, t) of two similar evolution p-Laplacian equations, both with source terms in a divergent …

This article concerns the effect of slow diffusion in two-species competition-diffusion problem
with spatially homogeneous nearly identical reaction terms. In this case all (nonnegative) …