• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.409-430
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• 2010

The present paper will be concerned to the investigation of the stress-strain field around the cavity that is loaded or partially loaded at the inner surface by the rotationally symmetric loading. The cavity of the spherical, cylindrical or elliptical shape is situated in a stressed elastic continuum, subjected to the gravitation field. As the contribution to the similar investigations, the paper introduces the new function of loading in the form of the infinite sine series. Besides, in this paper the solution of stresses around an oblong ellipsoid cavity, has been obtained using appropriate curvilinear elliptical coordinates. This analytical approach avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.