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Quasilinear and quadratic singularly perturbed Neumann’s problem. (English) Zbl 0937.34023
Boundary conditions of the form $$y'(a,\varepsilon)=0, y'(b,\varepsilon)=0$$ are considered along with singularly perturbed equations of the form $$\varepsilon y''=F(t,y,y')$$ on $$(a,b)$$. Existence and asymptotic behaviour of solutions are studied in the case when $F(t,y,y')=f(t,y)y'+g(t,y)\quad \text{or}\quad F(t,y,y')=f(t,y)y'{}^2+g(t,y).$
##### MSC:
 34B20 Weyl theory and its generalizations for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations
##### Keywords:
singular perturbation; Neumann problem
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