Browsing by Subject "Palais-Smale condition"

Now showing 1 - 3 of 3

Access status: Open Access ,
Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem
(2015) Klimczak, Liliana
We consider a nonlinear Neumann elliptic equation driven by a $p$-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.
Access status: Open Access ,
Existence result for hemivariational inequality involving p(x)-Laplacian
(2012) Barnaś, Sylwia
In this paper we study the nonlinear elliptic problem with $p(x)$-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102-129].
Access status: Open Access ,
On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative
(Wydawnictwa AGH, 2019) Bełdziński, Michał; Galewski, Marek
In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.