In this paper we investigate the existence of entropy solution for the following nonlinear elliptic equation involving p(x)-Laplacian type operator,−Δp(x)u+|u|p(x)−2u=μin a bounded set Ω⊂ℝN, coupled with a Dirichlet boundary condition. For right-hand side measure μ which admits a...

We consider a nonlinear parametric Dirichlet problem driven by the anisotropic p-Laplacian with the combined effects of “concave” and “convex” terms. The “superlinear” nonlinearity need not satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on the critical...

Multistable stochastic integrals on R, have been introduced quite recently in Falconer and Liu (2012); they are defined through their characteristic functions. Roughly speaking, in a neighborhood of an arbitrary point x∈R, such an integral can be viewed as a usual stable stochastic integral,...