Homogenization with jumping nonlinearities

1984 ◽  
Vol 138 (1) ◽  
pp. 211-221 ◽  
Author(s):  
L. Boccardo ◽  
T. Gallouet
Keyword(s):  
Jumping Nonlinearities

scholarly journals Sign-changing and multiple solutions for thep-Laplacian

2002 ◽  
Vol 7 (12) ◽  
pp. 613-625 ◽  
Author(s):  
Siegfried Carl ◽  
Kanishka Perera
Keyword(s):  
Positive Solution ◽  
Multiple Solutions ◽  
Negative Solution ◽  
Jumping Nonlinearities

We obtain a positive solution, a negative solution, and a sign-changing solution for a class ofp-Laplacian problems with jumping nonlinearities using variational and super-subsolution methods.

Periodic solutions of forced Liénard equations with jumping nonlinearities under nonuniform conditions

1988 ◽  
Vol 110 (3-4) ◽  
pp. 183-198 ◽  
Author(s):  
R. Iannacci ◽  
M.N. Nkashama ◽  
P. Omari ◽  
F. Zanolin
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Periodic Solutions ◽  
Homogeneous Problem ◽  
A Priori ◽  
Critical Values ◽  
Liénard Equations ◽  
Jumping Nonlinearities ◽  
Existence Of Periodic Solutions ◽  
Image Position

SynopsisThis paper is devoted to the existence of periodic solutions for the scalar forced Lienard differential equationThe key assumptions relate the asymptotic behaviour as x →± ∞of g(t; x)/x to the “critical values” of the positively 1-homogeneous problemNo condition on f, except continuity, is assumed. Our approach is based on Leray–Schauder degree techniques and a priori estimates.

scholarly journals Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz–Sobolev spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Q-Heung Choi ◽  
Tacksun Jung
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problems ◽  
Sobolev Spaces ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Degree Theory ◽  
Contraction Mapping Principle ◽  
Source Terms ◽  
Laplacian Eigenvalue ◽  
Jumping Nonlinearities

AbstractWe investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obtain these results by direct computations with the eigenvalues and the corresponding eigenfunctions for the fractional N-Laplacian eigenvalue problem in the fractional Orlicz–Sobolev spaces, the contraction mapping principle on the fractional Orlicz–Sobolev spaces and Leray–Schauder degree theory.

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