# Regularity and relaxed problems of minimizing biharmonic maps into spheres

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This paper is devoted to the continuity of the solution mapping for vector quasiequilibrium problems under mapping perturbations. We show that the solution mapping is upper semicontinuous and Hausdorff upper semicontinuous. Sufficient conditions for the lower semicontinuity and Hausdorff lower...

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We show the existence result of viable solutions to the differential inclusion áº‹(t) âˆˆ G(x(t)) + F(t, x(t)) x(t) âˆˆ S on [0, T], where F : [0, T] x H â†’ H (T > 0) is a continuous set-valued mapping, G : H â†’ H is a Hausdorff upper semi-continuous set-valued mapping such...

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In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped...

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We explicitly construct the Greenâ€™s function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Greenâ€™s function are of interest in their own right. In particular, the explicit representations for a solution to the...

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Let f be a transcendental meromorphic function and denote by J(f) the Julia set and by I(f) the escaping set. We show that if f has a direct singularity over infinity, then I(f) has an unbounded component and I(f)âˆ©J(f) contains continua. Moreover, under this hypothesis I(f)âˆ©J(f) has an...

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In this note, we prove the existence of positive solutions to a class of biharmonical systems. Our main ingredients are proving a Liouville type result for biharmonical system in â„ via the method of moving plane combined with integral inequality, and establishing a prior estimates for...

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In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

- Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity. Baishun Lai // Abstract & Applied Analysis;2014, p1
We study the following semilinear biharmonic equation Î”Â²u = Î»/1 - u, in B, and u = âˆ‚u/âˆ‚n = 0, on âˆ‚B, where B is the unit ball in â„n and n is the exterior unit normal vector. We prove the existence of Î»* > 0 such that for Î» âˆˆ (0, Î»*) there exists a...