(Super)Critical nonlocal equations with periodic boundary conditions

Ambrosio, Vincenzo; Mawhin, Jean; Bisci, Giovanni Molica

doi:10.1007/s00029-018-0398-y

Cited by 11 publications

(2 citation statements)

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“…We intend to study a challenging problem related to Yamabe-type equations on non-compact Riemannian manifolds by using a suitable group-theoretical approach based on the Palais criticality principle (see, for related topics, the papers [39][40][41]) under the asymptotically condition (As H,g R ) on the Ricci curvature. In particular, motivated by the recent results obtained in [1,38,46,47] we are interested on the existence of multiple solutions for the following critical equation…”

Section: A Local Minimum Geometrymentioning

confidence: 99%

Elliptic problems on complete non-compact Riemannian manifolds with asymptotically non-negative Ricci curvature

Bisci¹,

Secchi²

2018

Preprint

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In this paper we discuss the existence and non-existence of weak solutions to parametric equations involving the Laplace-Beltrami operator ∆ g in a complete noncompact d-dimensional (d ≥ 3) Riemannian manifold (M, g) with asymptotically non-negative Ricci curvature and intrinsic metric d g . Namely, our simple model is the following problemwhere V is a positive coercive potential, α is a positive bounded function, λ is a real parameter and f is a suitable continuous nonlinear term. The existence of at least two non-trivial bounded weak solutions is established for large value of the parameter λ requiring that the nonlinear term f is non-trivial, continuous, superlinear at zero and sublinear at infinity. Our approach is based on variational methods. No assumptions on the sectional curvature, as well as symmetry theoretical arguments, are requested in our approach.

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Section: A Local Minimum Geometrymentioning

confidence: 99%

Elliptic problems on complete non-compact Riemannian manifolds with asymptotically non-negative Ricci curvature

Bisci¹,

Secchi²

2018

Preprint

Self Cite

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“…We note that the Kirchhoff problems considered in literature are set in R N or in bounded domains with homogeneous boundary conditions. On the other hand, in these years the existence and multiplicity of periodic solutions for subcritical and critical problems have been studied in [5][6][7][8]11] and the references therein.…”

Section: Introductionmentioning

confidence: 99%