Volume 24, Number 2, April–June 2018
|Page(s)||569 - 578|
|Published online||26 January 2018|
Department of Mathematics, University of Craiova,
200585 Craiova, Romania
2 Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania
3 Department of Mathematics and Computer Science, University Politehnica of Bucharest, 060042 Bucharest, Romania
4 “Simion Stoilow” Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
5 Department of MathematicsUniversity of Pecs, 7624 Pécs, Hungary
a Corresponding author: firstname.lastname@example.org
Revised: 17 June 2017
Accepted: 19 June 2017
Let Ω ⊂ ℝN (N ≥ 2) be a bounded domain with smooth boundary. We show the existence of a positive real number λ* such that for each λ ∈ (0, λ*) and each real number p > N the equation −Δp u = λeu in Ω subject to the homogeneous Dirichlet boundary condition possesses a nonnegative solution up. Next, we analyze the asymptotic behavior of up as p → ∞ and we show that it converges uniformly to the distance function to the boundary of the domain.
Mathematics Subject Classification: 35D30 / 35D40 / 35J60 / 47J30 / 46E30
Key words: Weak solutionviscosity solution / nonlinear elliptic equations / asymptotic behavior / distance function to the boundary
Corresponding author: Mihai Mihăilescu, Department of Mathematics, University of Craiova, 200585 Craiova, Romania. E-mail: email@example.com.
The research of M. Mihăilescu was partially supported by an UBB Advanced Fellowship-Intern granted by Star-UBB Institute, no. CNFIS-FDI-2016-0056. D. Stancu−Dumitru has been partially supported by CNCS-UEFISCDI Grant No. PN-III-P1-1.1-PD-2016-0202. The research of C. Varga has been partially supported by OTKA (grant no. K 115926)..
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.