Weakly nonlocal boundary value problems with application to geology

IF 0.7 Q3 MATHEMATICS, APPLIED Differential Equations & Applications Pub Date : 2021-03-16 DOI:10.7153/DEA-2021-13-12
D. Maroncelli, E. Collins
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引用次数: 1

Abstract

In many cases, groundwater flow in an unconfined aquifer can be simplified to a one-dimensional Sturm-Liouville model of the form: \begin{equation*} x''(t)+\lambda x(t)=h(t)+\varepsilon f(x(t)),\hspace{.1in}t\in(0,\pi) \end{equation*} subject to non-local boundary conditions \begin{equation*} x(0)=h_1+\varepsilon\eta_1(x)\text{ and } x(\pi)=h_2+\varepsilon\eta_2(x). \end{equation*} In this paper, we study the existence of solutions to the above Sturm-Liouville problem under the assumption that $\varepsilon$ is a small parameter. Our method will be analytical, utilizing the implicit function theorem and its generalizations.
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弱非局部边值问题及其在地质学中的应用
在许多情况下,无承压含水层中的地下水流动可以简化为一维Sturm-Liouville模型,其形式为:\begin{equation*} x''(t)+\lambda x(t)=h(t)+\varepsilon f(x(t)),\hspace{.1in}t\in(0,\pi) \end{equation*}在非局部边界条件下\begin{equation*} x(0)=h_1+\varepsilon\eta_1(x)\text{ and } x(\pi)=h_2+\varepsilon\eta_2(x). \end{equation*}。本文在$\varepsilon$为小参数的假设下,研究上述Sturm-Liouville问题解的存在性。我们的方法是解析式的,利用隐函数定理及其推广。
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期刊最新文献
Weakly nonlocal boundary value problems with application to geology Multiplicity results for critical fractional equations with sign-changing weight functions Unique solvability of fractional quadratic nonlinear integral equations Existence of solutions for a coupled system of Caputo type fractional-order differential inclusions with non-separated boundary conditions on multivalued maps Existence of solutions to nonlinear Sturm-Liouville problems with large nonlinearities
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