Abstract
The paper presents existence results for solutions to a nonsmooth hyperbolic problem in the form of a hemivariational inequality separately in the nonresonant and resonant cases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Ahmad, A. C. Lazer and J. L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933–944.
V. Barbu, Necessary conditions for multiple integral problems in the calculus of variations, Math. Ann. 260 (1982), 175–189.
V. Barbu and N. H. Pavel, Periodic optimal control in Hilbert spaces, Appl. Math. Optimiz. 33 (1996), 169–188.
H. Brézis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull (New Series) Amer. Math. Soc. 8 (1983), 409–426.
K. C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102–129.
F. H. Clarke, Nonsmooth analysis and optimization, Wiley & Sons, New York, 1984.
D. Goeleven, D. Motreanu and P. D. Panagiotopoulos, Eigenvalue problems for variational-hemivariational inequalities at resonance, Nonlin. Anal. TMА, 33 (1998), 161–185
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609–623.
P. D. Panagiotopoulos, Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993
P. H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, in: Nonlinear Analysis: A collection of papers in honor of E. Röthe, Academic Press, New York, 1978, pp. 161–177.
P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc., Providence, R. I., 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this chapter
Cite this chapter
Goeleven, D., Motreanu, D. (2001). Hyperbolic Hemivariational Inequality and Nonlinear Wave Equation with Discontinuities. In: Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M. (eds) From Convexity to Nonconvexity. Nonconvex Optimization and Its Applications, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0287-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0287-2_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7979-9
Online ISBN: 978-1-4613-0287-2
eBook Packages: Springer Book Archive