Existence and boundary behavior of positive solutions for a Sturm-Liouville problem
| Autor: | Samia Zermani, Syrine Masmoudi |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
positive solutions
Measurable function lcsh:T57-57.97 General Mathematics 010102 general mathematics Mathematical analysis Boundary (topology) Sturm–Liouville theory Green's function Fixed point 01 natural sciences Prime (order theory) 010101 applied mathematics Combinatorics Karamata regular variation theory symbols.namesake nonlinear Sturm-Liouville problem lcsh:Applied mathematics. Quantitative methods symbols Differentiable function Uniqueness 0101 mathematics Mathematics |
| Zdroj: | Opuscula Mathematica, Vol 36, Iss 5, Pp 613-629 (2016) |
| ISSN: | 1232-9274 |
| DOI: | 10.7494/opmath.2016.36.5.613 |
| Popis: | In this paper, we discuss existence, uniqueness and boundary behavior of a positive solution to the following nonlinear Sturm-Liouville problem \[\begin{aligned}&\frac{1}{A}(Au^{\prime })^{\prime }+a(t)u^{\sigma}=0\;\;\text{in}\;(0,1),\\ &\lim\limits_{t\to 0}Au^{\prime}(t)=0,\quad u(1)=0,\end{aligned}\] where \(\sigma \lt 1\), \(A\) is a positive differentiable function on \((0,1)\) and \(a\) is a positive measurable function in \((0,1)\) satisfying some appropriate assumptions related to the Karamata class. Our main result is obtained by means of fixed point methods combined with Karamata regular variation theory. |
| Databáze: | OpenAIRE |
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