Weakly Nonlocal Boundary Value Problems with Application to Geology
Abstract
In many cases, groundwater flow in an unconfined aquifer can be simplified to a one-dimensional Sturm-Liouville model of the form: equation* x''(t)+λ x(t)=h(t)+ f(x(t)),.1int∈(0,π) equation* subject to non-local boundary conditions equation* x(0)=h1+η1(x) and x(π)=h2+η2(x). equation* In this paper, we study the existence of solutions to the above Sturm-Liouville problem under the assumption that is a small parameter. Our method will be analytical, utilizing the implicit function theorem and its generalizations.
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