A difference inequality and its application to nonlinear evolution equations

Mitsuhiro NAKAO

doi:10.2969/jmsj/03040747

Mitsuhiro NAKAO

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 4 Pages 747-762

DOI https://doi.org/10.2969/jmsj/03040747

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Published: 1978 Received: May 02, 1977 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. A. Levine, Growth of solutions of generalized nonlinear Euler-Poisson-Darboux equations, Arch. Rational Mech. Anal., 61 (1976), 77-89.
2) J. L. Lions, Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires, Dunod, Paris, 1969.
3) J. L. Lions and W. A. Strauss, Some non-linear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96.
4) M. Nakao, Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term, J. Math. Anal. Appl., 58 (1977), 336-343.
5) M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, Mem. Fac. Sci. Kyushu Univ., 30 (1976), 257-265.
6) M. Nakao, Decay of solutions of some nonlinear evolution equations, J. Math. Anal. Appl., 60 (1977), 542-549.
7) M. Nakao, Decay of classical solutions of a semilinear wave equation, Math. Rep. College Gen. Ed. Kyushu Univ., 11 (1977), 39-45.
8) M. Nakao, On bounded, periodic and almost periodic solutions for a system of nonlinear second order ordinary differential equations, J. Math. Anal. Appl, 61 (1977), 620-632.
9) J. Sather, The existence of a global classical solution of the initial boundary value problem for _??_u+u³=f, Arch. Rational Mech. Anal., 22 (1966), 292-307.
10) W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math., 19 (1966), 543-551.
11) M. Tsutsumi, Some evolution equations of second order, Proc. Japan Acad., 47 (1970), 950-955.

Right : [1] H. A. Levine, Growth of solutions of generalized nonlinear Euler-Poisson-Darboux equations, Arch. Rational Mech. Anal., 61 (1976), 77-89.
[2] J. L. Lions, Quelques Methodes de Resolution des Problemes aux Limites Non Lineaires, Dunod, Paris, 1969.
[3] J. L. Lions and W. A. Strauss, Some non-linear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96.
[4] M. Nakao, Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term, J. Math. Anal. Appl., 58 (1977), 336-343.
[5] M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, Mem. Fac. Sci. Kyushu Univ., 30 (1976), 257-265.
[6] M. Nakao, Decay of solutions of some nonlinear evolution equations, J. Math. Anal. Appl., 60 (1977), 542-549.
[7] M. Nakao, Decay of classical solutions of a semilinear wave equation, Math. Rep. College Gen. Ed. Kyushu Univ., 11 (1977), 39-45.
[8] M. Nakao, On bounded, periodic and almost periodic solutions for a system of nonlinear second order ordinary differential equations, J. Math. Anal. Appl., 61 (1977), 620-632.
[9] J. Sather, The existence of a global classical solution of the initial boundary value problem for _??_u+u³=f, Arch. Rational Mech. Anal., 22 (1966), 292-307.
[10] W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math., 19 (1966), 543-551.
[11] M. Tsutsumi, Some evolution equations of second order, Proc. Japan Acad., 47 (1970), 950-955.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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