In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.
@article{118945, author = {Dimitrios A. Kandilakis}, title = {Pseudomonotonicity and nonlinear hyperbolic equations}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {463-469}, zbl = {0940.35123}, mrnumber = {1485068}, language = {en}, url = {http://dml.mathdoc.fr/item/118945} }
Kandilakis, Dimitrios A. Pseudomonotonicity and nonlinear hyperbolic equations. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 463-469. http://gdmltest.u-ga.fr/item/118945/
Analysis and Probability, Academic Press, NY, 1972.
Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Inter. Pub. Leyden, The Netherlands. | MR 0390843 | Zbl 0328.47035
Pseudomonotonicity and the Leray-Lions condition, Diff. and Integral Equations 6 (1993), 37-45. (1993) | MR 1190164
Quelques Methodes de Resolution des Problemes aux Limites Non-Lineaires, Dunod, Paris, 1969. | MR 0259693 | Zbl 0248.35001
Existence of solutions for second order evolution inclusions, J. Appl. Math and Stoch. Anal. 4, vol. 7 (1994), pp.525-535. | MR 1310925 | Zbl 0857.34028
Nonlinear evolution equations in Banach spaces, J. Diff. Equations 9 (1971), 608-618. (1971) | MR 0300172 | Zbl 0227.47043
Nonlinear Functional Analysis and its Applications, Springer Verlag, NY, 1990. | Zbl 0794.47033