Analysis of search-extension method for finding multiple solutions of nonlinear problem

2008 ◽  
Vol 51 (1) ◽  
pp. 42-54 ◽  
Author(s):  
ChuanMiao Chen ◽  
ZiQing Xie
Keyword(s):  
Nonlinear Problem ◽  
Multiple Solutions ◽  
Extension Method

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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