Multiple solutions for an asymptotically linear problem in

2004 ◽  
Vol 56 (1) ◽  
pp. 1-18
Author(s):  
A.M. Micheletti ◽  
C. Saccon
Keyword(s):  
Multiple Solutions ◽  
Linear Problem ◽  
Asymptotically Linear ◽  
Asymptotically Linear Problem

scholarly journals Periodic solutions for a fractional asymptotically linear problem

2018 ◽  
Vol 149 (03) ◽  
pp. 593-615
Author(s):  
Vincenzo Ambrosio ◽  
Giovanni Molica Bisci
Keyword(s):  
Neumann Boundary ◽  
Index Theory ◽  
Careful Analysis ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Degenerate Elliptic ◽  
Subcritical Nonlinearity ◽  
Fractional Spaces ◽  
Non Local ◽  
Asymptotically Linear Problem

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the pseudo-index theory developed by Bartolo, Benci and Fortunato [11] after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in the literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.

scholarly journals Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations onRN

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yu Duan ◽  
Chun-Lei Tang
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Multiple Solutions ◽  
Asymptotically Linear ◽  
Kirchhoff Type ◽  
Multiplicity Of Positive Solutions

The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameterλonRNis proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity andλ>0is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of three positive solutions.

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