A Non- Linear Hyperbolic Variational Inequality

Objective: In this paper we are concerned about the existence of solution for a nonlinear hyperbolic variational inequality in Sobolev space under certain conditions. Method: We discuss the penalty method and Gronwall’s inequality for the variational inequality. Results and Discussion: Using penalty method we obtain the existence of solutions for a nonlinear partial differential equation which was handled by Lions, J. (1997). Further results can be found in Ekeland,I. and Temam,R.(1976),Chipot,M.(1984) . Implications of the research: Apply in the first university years the application of a non- linear hyperbolic variational inequality to dynamic systems in all university careers and specialties as part of the management of the tools of Information and Communication Technology (TIC). Originality/Value: This paper also provides an alternative approach to Analysis of vibration amplitudes with generalized potentials with MATLAB.