On the Dirichlet problem associated with bounded perturbations of positively-(p, q)- homogeneous Hamiltonian systems

Fonda, Alessandro; Klun, Giuliano; Obersnel, Franco; Sfecci, Andrea

doi:10.1007/s11784-022-00980-7

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Lower and Upper Solutions1

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Cited by 3 publications

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“…We now provide the definitions of lower and upper solutions for problem (6), thus extending the ones given in [5][6][7]. Definition 6.…”

Section: Lower and Upper Solutionsmentioning

confidence: 99%

A Lower/Upper Solutions Result for Generalised Radial p-Laplacian Boundary Value Problems

et al. 2023

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We provide existence results to some planar nonlinear boundary value problems, in the presence of lower and upper solutions. Our results apply to a class of systems generalising radial elliptic equations driven by the p-Laplace operator, and to some problems involving the Laplace–Beltrami operator on the sphere. After extending the definition of lower and upper solutions to the planar system, we prove our results by a shooting method involving a careful analysis of the solutions in the phase plane.

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“…We now provide the definitions of lower and upper solutions for problem (6), thus extending the ones given in [5][6][7]. Definition 6.…”

Section: Lower and Upper Solutionsmentioning

confidence: 99%