Positive solution for the elliptic problems with sublinear and superlinear nonlinearities.
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We consider the linearized elasticity system in a multidomain of . This multidomain is the union of a horizontal plate with fixed cross section and small thickness , and of a vertical beam with fixed height and small cross section of radius . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When and tend to zero simultaneously, with , we identify the limit problem. This limit problem involves six junction conditions.