On positive solutions for a class of infinite semipositone problems

	On positive solutions for a class of infinite semipositone problems
International Journal of Nonlinear Analysis and Applications
مقاله 5، دوره 4، شماره 1، 2013، صفحه 49-54 اصل مقاله (338.84 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2013.25
نویسندگان
M. B. Ghaemi^* ¹؛ M. Choubin²
¹Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
²Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran
چکیده
We discuss the existence of a positive solution to the innite semipositone problem $$\Delta u=au-bu^\gamma-f(u)-\frac{c}{u^\alpha}, \quad x\in\Omega,\quad u=0, x\in\partial\Omega,$$ where $\Delta$ is the Laplacian operator, $\gamma>1, \alpha\in(0,1), a,b$ and $c$ are positive constants, $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary $\partial\Omega$, and $f : [0;1) \to \mathbb{R}$ is a continuous function such that $f(u)\to \infty$ as $u\to \infty$. Also we assume that there exist $A > 0$ and $\beta > 1$ such that $f(s) \leq As^\beta$, for all $s \geq 0$. We obtain our result via the method of sub- and supersolutions.
کلیدواژه‌ها
positive solution؛ Innite semipositone؛ Sub- and supersolutions
آمار تعداد مشاهده مقاله: 18,323 تعداد دریافت فایل اصل مقاله: 12,876

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