Browsing by Subject "nonlinear boundary conditions"

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Access status: Open Access ,
Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions
(Wydawnictwa AGH, 2019) Hai, D. D.; Wang, X.
We prove the existence of positive solutions for the $p$-Laplacian problem $\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}$ where $\phi (s)=|s|^{p-2}s$, $p \gt 1$, $H_{i}:\mathbb{R}\rightarrow\mathbb{R}$ can be nonlinear, $i=1,2$, $f:(0,\infty)\rightarrow \mathbb{R}$ is $p$-superlinear or $p$-sublinear at $\infty$ and is allowed be singular $(\pm\infty)$ at $0$, and $\lambda$ is a positive parameter.
Access status: Open Access ,
Positive solutions of boundary value problems with nonlinear nonlocal boundary conditions
(2016) Padhi, Seshadev; Pati, Smita; Hota, D. K.
We consider the existence of at least three positive solutions of a nonlinear first order problem with a nonlinear nonlocal boundary condition given by $\begin{aligned} x^{\prime}(t)& = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), \quad t \in [0,1],\\ \lambda x(0)& = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\quad \tau_j \in [0,1],\end{aligned}$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous; the nonlocal points satisfy $0 \leq \tau_1 \lt \tau_2 \lt \ldots \lt \tau_n \leq 1$ the nonlinear function $f_i$ and $\tau_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,\ldots ,m$ and $j = 1,2,\ldots ,n$ respectively, and $\lambda \gt 0$ is a positive parameter.