A uniqueness result for a class of infinite semipositone problems with nonlinear boundary conditions
Autor: | Amila Muthunayake, Ratnasingham Shivaji, D. D. Hai |
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Rok vydání: | 2021 |
Předmět: |
Class (set theory)
021103 operations research General Mathematics 010102 general mathematics 0211 other engineering and technologies 02 engineering and technology Function (mathematics) Operator theory Lambda 01 natural sciences Potential theory Nonlinear boundary conditions Theoretical Computer Science Combinatorics Matrix (mathematics) Uniqueness 0101 mathematics Analysis Mathematics |
Zdroj: | Positivity. 25:1357-1371 |
ISSN: | 1572-9281 1385-1292 |
DOI: | 10.1007/s11117-021-00820-x |
Popis: | We study positive solutions to the two-point boundary value problem: $$\begin{aligned} \begin{matrix} -u''=\lambda h(t) f(u)~;~(0,1) \\ u(0)=0\\ u'(1)+c(u(1))u(1)=0,\end{matrix} \end{aligned}$$ where $$\lambda >0$$ is a parameter, $$h \in C^1((0,1],(0,\infty ))$$ is a decreasing function, $$f \in C^1((0,\infty ),\mathbb {R}) $$ is an increasing concave function such that $$\lim \limits _{s \rightarrow \infty }f(s)=\infty $$ , $$\lim \limits _{s \rightarrow \infty }\frac{f(s)}{s}=0$$ , $$\lim \limits _{s \rightarrow 0^+}f(s)=-\infty $$ (infinite semipositone) and $$c \in C([0,\infty ),(0,\infty ))$$ is an increasing function. For classes of such h and f, we establish the uniqueness of positive solutions for $$\lambda \gg 1$$ . |
Databáze: | OpenAIRE |
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