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We prove the Hölder continuity of a homeomorphism f defined on a bounded domain Ω ⊂ ℝ n with Lipschitz boundary. The homeomorphism f is assumed to belong to a certain Orlicz–Sobolev class and to satisfy a distortion condition near the boundary. [ABSTRACT FROM AUTHOR]

Recently, the existence of at least two weak solutions for a Kirchhoff–type problem has been studied in [M. Makvand Chaharlang and A. Razani, Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition, Georgian Math. J. 28 2021, 3, 429–438]. Here, the existence of infinitely many solutions for nonlocal Kirchhoff-type systems including Dirichlet boundary conditions in Orlicz–Sobolev spaces is studied by using variational methods and critical point theory. [ABSTRACT FROM AUTHOR]

In this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces. [ABSTRACT FROM AUTHOR]

Based on a variational principle for smooth functionals defined on reflexive Banach spaces, the existence of at least one weak solution for a non-homogeneous Neumann problem in an appropriate Orlicz–Sobolev space is discussed. [ABSTRACT FROM AUTHOR]

We study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form ... div(a(x,t,u,∇u))+g(x,t,u,∇u)+H(x,t,∇u) = μ in Ω × (0,T), where the right-hand side belongs to L¹(QT) + Lp′(0,T;W-1,p′(Ω)) and b(x,u) is unbounded function of u, −div(a(x,t,u,∇u)) is a Leray-Lions type operator with growth |∇u|p-1 in ∇u. The critical growth condition on g is with respect to ∇u and there is no growth condition with respect to u, while the function H(x,t,∇u) grows as |∇u|p-1. [ABSTRACT FROM AUTHOR]

We prove the existence of a renormalized solution for the Dirichlet problem associated to the nonlinear elliptic equations - div a(x, u, ∇u) - div Φ(u) + g(x, u, ∇u) = f in Ω , in the general setting of Orlicz spaces, where Φ ∊ C0(R,RN), the function g has a natural growth with respect to its third argument and satisfies the sign condition while the datum f belongs to W-1EM(Ω). No Δ2-condition is needed for the considered N-functions. [ABSTRACT FROM AUTHOR]