Abstract
We study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet boundary data, in presence of a superlinear term. Starting from the well-known Ambrosetti–Rabinowitz condition, we consider different growth assumptions on the nonlinearity, all of superlinear type. We obtain three different existence results in this setting by using the Fountain Theorem, which extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.
Funding statement: The authors were supported by the SRA Program P1-0292-0101 Topology, Geometry and Nonlinear Analysis. The first and the third author were supported by the INdAM-GNAMPA Project 2015 Modelli ed equazioni non-locali di tipo frazionario. The third author was supported by the MIUR National Research Project Variational and Topological Methods in the Study of Nonlinear Phenomena and by FP7-IDEAS-ERC Starting Grant 2011 #277749 EPSILON (Elliptic Pde’s and Symmetry of Interfaces and Layers for Odd Nonlinearities), founded by the European Research Council (ERC).
Acknowledgements
The authors warmly thank the anonymous referee for her/his useful and nice comments on the paper.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks
Articles in the same Issue
- Frontmatter
- Behavior of bounds of singular integrals for large dimension
- The twofold way of super holonomy
- On mod p singular modular forms
- Martin boundary of unbounded sets for purely discontinuous Feller processes
- Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order
- Nontrivial solutions of superlinear nonlocal problems
- Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
- On regularization of vector distributions on manifolds
- The Addition Theorem for algebraic entropies induced by non-discrete length functions
- When are Zariski chambers numerically determined?
- Convexity theorems for semisimple symmetric spaces
- On amenability of groups generated by homogeneous automorphisms and their cracks