Uriel Kaufmann

On positive solutions for some semilinear periodic parabolic eigenvalue problems

For a bounded domain Ω in RN, N⩾2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Luλ=λg(x,t,uλ) in Ω×R, uλ=0 on ∂Ω×R. We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. (x,t)∈Ω×R satisfying some integrability conditions in (x,t) and ∫0Tesssupx∈Ωinfξ>0g(x,t,ξ)ξdt>0.

Strictly positive solutions for one-dimensional nonlinear problems involving the \(p\)-Laplacian

Let \(Ω\) be a bounded open interval, and let \(p>1\) and \(q∈(0,p-1)\). Let \(m∈L^{p′}(Ω)\) and \(0≤c∈L^{∞}(Ω)\). We study existence of strictly positive solutions for elliptic problems of the form \(-(|u′|^{p-2}u′)′+c(x)u^{p-1}=m(x)u^{q}\) in \(Ω, u=0\) on \(∂Ω\). We mention that our results are new even in the case \(c≡0\). 10.1017/S0004972713000725

One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign

Abstract Let Ω be a bounded open interval, let p > 1

Existence of Strictly Positive Solutions for Sublinear Elliptic Problems in Bounded Domains

{p>1}

INHOMOGENEOUS PERIODIC PARABOLIC PROBLEMS WITH INDEFINITE DATA

and γ > 0

Loop Type Subcontinua of Positive Solutions for Indefinite Concave-Convex Problems

{\gamma>0}

On principal eigenvalues for periodic parabolic problems with optimal condition on the weight function

, and let m : Ω → ℝ

On strictly positive solutions for some semilinear elliptic problems

{m:\Omega\rightarrow\mathbb{R}}

On Dirichlet problems with singular nonlinearity of indefinite sign

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 problems of the form - ( | u ′ | p - 2 ⁢ u ′ ) ′ = m ⁢ ( x ) ⁢ u - γ

Strictly positive solutions for one-dimensional nonlinear elliptic problems

{-(|u^{\prime}|^{p-2}u^{\prime})^{\prime}=m(x)u^{-\gamma}}