For an initial value problem u'''(x) = g(u(x)), u(0) = u'(0) = u''(0) = 0, x > 0, some theorems on existence and uniqueness of solutions are established.
@article{bwmeta1.element.bwnjournal-article-apmv59z3p215bwm, author = {Wojciech Mydlarczyk}, title = {An initial value problem fora third order differential equation}, journal = {Annales Polonici Mathematici}, volume = {60}, year = {1994}, pages = {215-223}, zbl = {0808.34004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p215bwm} }
Wojciech Mydlarczyk. An initial value problem fora third order differential equation. Annales Polonici Mathematici, Tome 60 (1994) pp. 215-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p215bwm/
[000] [1] P. J. Bushell and W. Okrasiński, Uniqueness of solutions for a class of nonlinear Volterra integral equations with convolution kernel, Math. Proc. Cambridge Philos. Soc. 106 (1989), 547-552. | Zbl 0689.45013
[001] [2] G. Gripenberg, Unique solutions of some Volterra integral equations, Math. Scand. 48 (1981), 59-67. | Zbl 0463.45002
[002] [3] W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, ibid. 68 (1991), 83-88. | Zbl 0701.45002
[003] [4] W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal. 22 (1991), 1007-1015. | Zbl 0735.45005
[004] [5] W. Okrasiński, Nontrivial solutions for a class of nonlinear Volterra equations with convolution kernel, J. Integral Equations Appl. 3 (1991), 399-409. | Zbl 0745.45001