# Bernstein-type theorem for ϕ-Laplacian

In this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth condition. Our result is based on a priori bounds for the solution and homotopical invariance of the Leray–Schauder degree.
 Keywords A PRIORI BOUNDS BOUNDARY VALUE PROBLEM FIXED POINT LERAY–SCHAUDER DEGREE Φ -LAPLACIAN Publication year 2019 Publication language angielski Journal title / conference title Fixed Point Theory and Applications Page numbers [from-to] 1 - 9 Author (3) Jakub Maksymiuk Jakub Ciesielski Maciej Starostka Organization unit Katedra Analizy Nieliniowej i Statystyki Faculty Wydział Fizyki Technicznej i Matematyki Stosowanej