Singular perturbation, multiple solutions and hysteresis in a nonlinear problem

1977 ◽  
pp. 50-76 ◽  
Author(s):  
C. M. Brauner ◽  
B. Nicolaenko
Keyword(s):  
Singular Perturbation ◽  
Nonlinear Problem ◽  
Multiple Solutions

Higher Order Approximations in Stress Analysis of Submarine Pipelines

1980 ◽  
Vol 102 (4) ◽  
pp. 190-196 ◽  
Author(s):  
Ibrahim Konuk
Keyword(s):  
Singular Perturbation ◽  
Stress Analysis ◽  
Nonlinear Problem ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Higher Order ◽  
Two Dimensional ◽  
Singular Perturbation Technique ◽  
Programmable Calculator

A unified three-dimensional formulation of the pipeline or riser problems is developed by following the rod theories. A rigorous singular perturbation technique is used to solve the associated two-dimensional nonlinear problem. The results can be used with a programmable calculator.

scholarly journals Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions

2016 ◽  
Vol 34 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Mohammed Berrajaa ◽  
Omar Chakrone ◽  
Fatiha Diyer ◽  
Okacha Diyer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Minimization Method ◽  
The First Eigenvalue

In this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin.

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