A+ CATEGORY SCIENTIFIC UNIT

Boundary value problems for nonlinear perturbations of some $\phi$-Laplacians

Volume 77 / 2007

J. Mawhin Banach Center Publications 77 (2007), 201-214 MSC: Primary 34B15; Secondary 47H10. DOI: 10.4064/bc77-0-15

Abstract

This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form $$ (\phi(u'))' = f(t,u,u') $$ submitted to various boundary conditions. In the equation, $\phi : \mathbb R \to \left]-a,a\right[$ is a homeomorphism such that $\phi(0) = 0$. An important motivation is the case of the curvature operator, where $\phi(s) = s/\sqrt{1 + s^2}$. The problems are reduced to fixed point problems in suitable function space, to which Leray–Schauder theory is applied.

Authors

  • J. MawhinUniversité Catholique de Louvain
    Département de mathématique
    Chemin du Cyclotron, 2
    B-1348 Louvain-la-Neuve, Belgique
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image