On the existence of solutions of one-dimensional fourth-order equations-Reference-Cited by-同舟云学术

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On the existence of solutions of one-dimensional fourth-order equations

Published:2020-11-20 Issue:11 Volume:72 Page:1575-1588
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Shokooh S.,Afrouzi G. A.,Hadjian A.

Abstract

UDC 517.9 Using variational methods and critical point theorems, we prove the existence of nontrivial solutions for one-dimensional fourth-order equations. Multiplicity results are also pointed out.

Publisher

Institute of Mathematics National Academy of Sciences of Ukraine

Reference24 articles.

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2. A. Ambrosetti, P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14, 349 – 381 (1973), https://doi.org/10.1016/0022-1236(73)90051-7

3. A. Averna, G. Bonanno, Three solutions for a quasilinear two-point boundary-value problem involving the onedimensional p-Laplacian, Proc. Edinburgh Math. Soc., 47, no. 2, 257 – 270 (2004), https://doi.org/10.1017/S0013091502000767

4. Z. Bai, Positive solutions of some nonlocal fourth-order Boundary-value problem, Appl. Math. and Comput., 215, no. 12, 4191 – 4197 (2010), https://doi.org/10.1016/j.amc.2009.12.040

5. G. Bonanno, A critical point theorem via the Ekeland variational principle, Nonlinear Anal., 75, no. 5, 2992 – 3007 (2012), https://doi.org/10.1016/j.na.2011.12.003

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