Bernstein-type theorem for ϕ-LaplacianIn 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.A PRIORI BOUNDSBOUNDARY VALUE PROBLEMFIXED POINTLERAY–SCHAUDER DEGREEΦ -LAPLACIAN2019angielskiBernstein-type theorem for ϕ-Laplacian1 - 9Jakub Maksymiuk Jakub Ciesielski Maciej Starostka