Search results for: Φ -LAPLACIAN

• Clarke duality for Hamiltonian systems with nonstandard growth

  Publication

  • S. Acinas
  • J. Maksymiuk
  • F. Mazzone

  - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS - Year 2019

  We consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.

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• Bernstein-type theorem for ϕ-Laplacian

  Publication

  • J. Maksymiuk
  • J. Ciesielski
  • M. Starostka

  - Fixed Point Theory and Applications - Year 2019

  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...

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