On the Dirichlet problem for weakly non-linear elliptic partial differential equations

Abstract

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

The Fučik spectrum of the p-Laplace equations with different weights and its resonance problems

“…China. 2 School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, P.R. China.…”

On the Fučík spectrum of the scalar p-Laplacian with indefinite integrable weights

“…All authors read and approved the final manuscript. 1 Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, People's Republic of China. 2 Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China.…”

A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions

“…In the related literature, starting with the pioneering work of Dancer [12,13] and Fucik [18], there has been a large amount of papers to describe the dynamics of (1.5). Despite its simplicity, the dynamical behaviour of (1.5) has surprisingly a very rich structure.…”