Browsing by Subject "mountain pass theorem"
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Item type:Article, Access status: Open Access , Existence of solutions for a doubly critical Schrödinger-Poisson system on the first Heisenberg group(Wydawnictwa AGH, 2026) Ma, Xueyan; Shi, Shaoyun; Song, YueqiangThis work is devoted to the study of a class of Schrödinger-Poisson system with doubly critical growth on the first Heisenberg group. Utilizing the concentration-compactness principle associated with classical Sobolev space on the Heisenberg group and mountain pass theorem, we prove that the system admits multiple nontrivial solutions.Item type:Article, Access status: Open Access , Existence result for hemivariational inequality involving p(x)-Laplacian(2012) Barnaś, SylwiaIn 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].Item type:Article, Access status: Open Access , On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian(2014) Smejda, Joanna; Wieteska, RenataIn this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.