In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a ...

We study Lotka-Volterra models with fractional Laplacian. To do this we study in detail the logistic problem and show that the sub-supersolution method works for both the scalar problem and for systems. We apply this method ...

Let Ω be a smooth bounded domain in RN and let m be a possibly discontinuous and unbounded function that changes sign in Ω. Let f : [0,∞) → [0,∞) be a nondecreasing continuous function such that k1 ξp ≤ f (ξ) ≤ k2 ξp for ...

We study the existence and nonexistence of strictly positive solutions for the elliptic problems -- in a bounded open interval, with zero boundary conditions, where -- is a strongly uniformly elliptic differential operator, ...

In this work, we present results of existence, non-existence and multiplicity of positive solutions to elliptic problems involving the fractional p-Laplacian operator and the fractional Laplacian in the critical case, ...

Let Ω be a smooth bounded domain in RN, N≥1, let m,n be two nonnegative functions defined in Ω and let ϕ:RN→RN be a continuous and strictly monotone mapping. We consider the existence and nonexistence of positive solutions ...