TWO JUMPING NONLINEAR TERMS AND A NONLINEAR WAVE EQUATION

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Published: Nov 15, 2009
DOI: https://doi.org/10.14403/jcms.2009.22.4.675
Keywords:
Mountain Pass theorem, variational reduction method, nonlinear wave equation
Mathematics Subject Classification (2020):
Primary 35B38, 35B10, 35L05

Main Article Content

Tacksun Jung
Department of Mathematics, Kunsan National University
Q-Heung Choi
Department of Mathematics Education, Inha University

Abstract





We find the multiple nontrivial solutions of the equation of the form utt − uxx = b1[(u + 1)+ − 1] + b2[(u + 2)+ − 2] with Dirichlet boundary condition. Here we reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions.





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Article Details

Issue
Vol. 22 No. 4 (2009)
Section
Articles