Coercive and noncoercive nonlinear Neumann problems with indefinite potential
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Nikolaos S. Papageorgiou
Abstract
We consider nonlinear Neumann problems driven by a nonhomogeneous differential operator and an indefinite potential. In this paper we are concerned with two distinct cases. We first consider the case where the reaction is (p-1)-sublinear near ±∞ and (p-1)-superlinear near zero. In this setting the energy functional of the problem is coercive. In the second case, the reaction is (p-1)-superlinear near ±∞ (without satisfying the Ambrosetti–Rabinowitz condition) and has a (p-1)-sublinear growth near zero. Now, the energy functional is indefinite. For both cases we prove “three solutions theorems” and in the coercive setting we provide sign information for all of them. Our approach combines variational methods, truncation and perturbation techniques, and Morse theory (critical groups).
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
Articles in the same Issue
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
