We study the behaviour of the nonlinear criticalp-heat equation (and the related stationaryp-
laplacian equation)[formula] where− Δpu≡− div (|∇ u| p− 2∇ u), f (x)⩾ 0 verifying …

(−∆ pu= fλ (u), in Ω u| δΩ= 0,(1.1) where fλ (u)=| u| r− 2u+ λ| u| q− 2u with 1< q< p< r< p∗, λ>
0 and Ω a smooth bounded domain of RN. Using standard variational methods (local …

This lectures notes are a review of some contributions to the theory of Quasilinear Elliptic
Equations with a reaction term. We study the existence, multiplicity, positivity of solutions …

The proof of Theorem 1.1 is carried out in Section 2. A solution u= bifurcating from u= 0 is
found as a local minimum of f=, while a second solution u~= is obtained by using the …

Existence and multiplicity for negative solutions of k-Hessian equations - ScienceDirect Skip to
main contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …

Consider the Dirichlet problem for the parabolic equation u_t=Δu+f(x,t,u) in Ω*(0,∞), where
Ω is a bounded domain in R^n and f has superlinear subcritical growth in u. If f is …

This book derives new Hardy inequalities with double singular weights-at an interior point
and on the boundary of the domain. We focus on the optimality of Hardy constant and on its …

In this note, we revisit a class of p-Laplacian boundary value problems. By means of the
Leggett–Williams fixed-point theorem, we establish the existence of at least three positive …

We deal with a class of-Laplacian Dirichlet boundary-value problems where the combined
effects of 'sublinear'and 'superlinear'growths allow us to establish the existence of at least …

Abstract Let N≥2, B_R⊂\mathbbR^N denote the open ball of radius R about the origin. Let
f:0,∞)→0,∞) be a continuous map which behaves like e^s^p for some p∈1,NN-1 as s→∞ …