Fourth-Order Problems

Adams, R.A., John Fournier, J.F.: Sobolev Spaces. Volume 140 of Pure and Applied Mathematics (Amsterdam), 2nd edn. Elsevier/Academic, Amsterdam (2003)Google Scholar

Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Computer Science and Applied Mathematics. Academic [Harcourt Brace Jovanovich, Publishers], New York (1983). Translated from the German by Jon RokneCrossRefGoogle Scholar

Breuer, B., Horák, J., McKenna, P.J., Plum, M.: A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam. J. Differ. Equ. 224(1), 60–97 (2006)MathSciNetCrossRefGoogle Scholar

Chen, Y., McKenna, P.J.: Travelling waves in a nonlinearly suspended beam: some computational results and four open questions. Philos. Trans. R. Soc. Lond. Ser. A 355(1732), 2175–2184 (1997)MathSciNetCrossRefGoogle Scholar

Grillakis, M., Shatah, J., Strauss, W.: Stability theory of solitary waves in the presence of symmetry. I. J. Funct. Anal. 74(1), 160–197 (1987)MathSciNetCrossRefGoogle Scholar

Grillakis, M., Shatah, J., Strauss, W.: Stability theory of solitary waves in the presence of symmetry. II. J. Funct. Anal. 94(2), 308–348 (1990)MathSciNetCrossRefGoogle Scholar

Nagatou, K., Plum, M., McKenna, P.J.: Orbital stability investigations for travelling waves in a nonlinearly supported beam. J. Differ. Equ. 268(1), 80–114 (2019). https://doi.org/10.1016/j.jde.2019.08.008 MathSciNetCrossRefGoogle Scholar

Santra, S., Wei, J.: Homoclinic solutions for fourth order traveling wave equations. SIAM J. Math. Anal. 41(5), 2038–2056 (2009)MathSciNetCrossRefGoogle Scholar

Smets, D., van den Berg, J.B.: Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations. J. Differ. Equ. 184(1), 78–96 (2002)MathSciNetCrossRefGoogle Scholar

van den Berg, J.B., Breden, M., Lessard, J.-P., Murray, M.: Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof. J. Differ. Equ. 264(5), 3086–3130 (2018)MathSciNetCrossRefGoogle Scholar