Geodesic
Boundary-value problem for a second-order nonlinear equation with delta-like potential
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 177-190

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A Dirichlet nonlinear problem for a second-order equation is considered on an interval. The problem is perturbed by the delta-like potential $\varepsilon^{-1}Q\left(\varepsilon^{-1}x\right)$, where the function $Q(\xi)$ is compactly supported and $0\varepsilon\ll1$. A solution of this boundary-value problem is constructed with accuracy up to $O(\varepsilon)$ with the use of the method of matched asymptotic expansions. The obtained asymptotic approximation is validated by means of the fixed-point theorem. All types of boundary conditions are considered for a linear boundary-value problem.
Keywords: second-order equation; delta-like potential; small parameter; asymptotics. 
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     title = {Boundary-value problem for a second-order nonlinear equation with delta-like potential},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a17/}
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F. Kh. Mukminov; T. R. Gadylshin. Boundary-value problem for a second-order nonlinear equation with delta-like potential. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 177-190. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a17/