In this paper we study a class of double phase problems involving critical growth, namely−div(|∇u|p−2∇u+μ(x)|∇u|q−2∇u)=λ|u|ϑ−2u+|u|p⁎−2uin Ω,u=0on ∂Ω, where Ω⊂RN is bounded Lipschitz domain, 1<ϑ0, respectively. Based on variational topol...

We study the ground state solutions for following p&amp;q‐Laplacian equation where is a parameter large enough, with denotes ‐Laplacian operator, and . Under some assumptions periodic potential , weight function nonlinearity without Ambrosetti–Rabinowitz condition, we show above has solution.

We consider the p-Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p →∞.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit problem as p → 1.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p → ∞.

We obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional p−Laplacian operator and nonlinearities at critical growth.

Let T be a time scale. We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with p-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem wi...

In this paper we study eigenvalue problems for hemivariational inequalities driven by the p-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative p-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and ...