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Strictly positive solutions for one dimensional nonlinear elliptic problems
(2014)
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, ...
One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign
(2016)
Let Ω be a bounded open interval, let p > 1 and γ >, and let m : Ω → ℝ be a function that may change sign in Ω. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular ...
Decay bounds for nonlocal evolution equations in Orlicz spaces
(2016)
We show decay bounds of the form ∫Rd φ(u (x, t)) dx ≤ Ct−μ for integrable and bounded solutions to the nonlocal evolution equation ut(x, t) = ∫Rd J(x, y)G(u(y, t) − u(x, t))(u(y, t) − u(x, t)) dy + f (u(x, t)). Here G is ...
On Dirichlet problems with singular nonlinearity of indefinite sign
(2015)
Let Ω be a smooth bounded domain in RN , N ≥ 1, let K, M be two nonnegative functions and let α, γ > 0. We study existence and nonexistence of positive solutions for singular problems of the form −Δu = K(x)u−α − λM (x)u−γ ...
Existence of strictly positive solutions for sublinear elliptic problems in bounded domains
(2014)
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 ...