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Boundary value problems for nonlinear perturbations of some ϕ-Laplacians

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Mawhin J.

Banach Center Publications

2007

tom 77

nr 1

201-214

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 (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder theory is applied.

Ograniczanie wyników

1 Banach Center Publications

1 Mawhin J.

1 2007

Wyniki wyszukiwania

Boundary value problems for nonlinear perturbations of some ϕ-Laplacians