Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space

By C. Bereanu, Petru Jebelean, Pedro J. Torres. 2013

145 citations recorded by the source corpus.

Abstract In this paper, by using Leray–Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C 1 -functionals, we obtain existence of classical positive radial solutions for Dirichlet problems of type div ( ∇ v 1 − | ∇ v | 2 ) + f ( | x | , v ) = 0 in B ( R ) , v = 0 on ∂ B ( R ) . Here, B ( R ) = { x ∈ R N : | x | R } and f : [ 0 , R ] × [ 0 , α ) → R is a continuous function, which is positive on ( 0 , R ] × ( 0 , α ) .

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/64a10b7bd4013002fbd5cd7e51f408de55833bdb

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In Applied Mathematics

Citations in the corpus

The Dirichlet Problem with Mean Curvature Operator in Minkowski Space – a Variational Approach (2014, background): “Notice that the radial situation is treated in [7].”
Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space (2013, methodology): “Using a variational type argument, in [8] it is shown that if”
Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball (2016, background): “It also yields a completion of the recent papers [3] and [4].”
Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space (2013, unknown): “Our aim here is indeed to extend to a genuine PDE setting what has been obtained in [6], for the one-dimensional problem, and in [3], [4], [7], for the radially symmetric problem in a ball.”
Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation (2012, background): “After completing this paper we became aware of the recent preprint [4], where the existence of a positive radial solution of (2) in a ball Ω has been discussed, assuming conditions on f that guarantee the existence of a positive minimizer for the associated action functional at a negative level: the”
Global structure of radial positive solutions for a prescribed mean curvature problem in a ball (2014, background): “Very recently, Bereanu, Jebelean and Torres [7] used Leray-Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C1-functionals, proved existence of classical positive radial solutions for Dirichlet problems Mv + f(|x|, v) = 0 in B(R), v = 0 on ∂B(R), ”