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Annali di Matematica Pura ed Applicata : Volume 196

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Stability for quantitative photoacoustic tomographywith well-chosen illuminations

Submanifolds with nonpositive extrinsic curvature

Asymptotically linear fractional p-Laplacian equations

Stability of odd periodic solutions in a resonant oscillator

Extensions of degree $$p^\ell $$ of a p-adic field

Superlinear Neumann problems with the p-Laplacian plus an indefinite potential

Algebraic approximation preserving dimension

Comments on Sampson’s approach toward Hodge conjecture on Abelian varieties

Generalized fundamental matrices as Grassmann tensors

Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces

Hardy–Sobolev-type inequalities with monomial weights

On critical exponents for Lane–Emden–Fowler-type equations with a singular extremal operator

Time periodic traveling curved fronts of bistable reaction–diffusion equations in $${\mathbb {R}}^3$$

Globally stable quasistatic evolution for strain gradient plasticity coupled with damage

Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension

Periodic solutions of an asymptotically linear Dirac equation

A Landau’s theorem in several complex variables

Double loop algebras and elliptic root systems

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Superlinear Neumann problems with the p-Laplacian plus an indefinite potential

Content Provider	Springer Nature Link
Author	Mugnai, Dimitri Fragnelli, Genni Papageorgiou, Nikolaos S.
Copyright Year	2016
Abstract	We consider nonlinear Neumann problems driven by the p-Laplacian plus an indefinite potential and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. First, we prove an existence theorem, and then, under stronger conditions on the reaction, we prove a multiplicity theorem producing three nontrivial solutions. Then, we examine parametric problems with competing nonlinearities (concave and convex terms). We show that for all small values of the parameter $$\lambda >0$$ , the problem has five nontrivial solutions and if $$p=2$$ (semilinear equation), there are six nontrivial solutions. Finally, we prove a bifurcation result describing the set of positive solutions as the parameter $$\lambda >0$$ varies.
Ending Page	517
Page Count	39
Starting Page	479
File Format	PDF
ISSN	03733114
e-ISSN	16181891
Journal	Annali di Matematica Pura ed Applicata
Issue Number	2
Volume Number	196
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-06-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multiple solutions Bifurcation theorem Neumann problem p-Laplacian Critical groups Competing nonlinearities Variational methods for second-order elliptic equations Superlinear reaction Nonlinear boundary value problems for linear elliptic equations Mathematics Indefinite potential Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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