Existence of infinitely many mountain pass solutions for some fourth-order boundary value problems with a parameter

DOI10.1016/j.na.2009.06.005zbMath1191.34018OpenAlexW2025651545MaRDI QIDQ1044492

Ji Hui Zhang, Yingchen Yang

Publication date: 18 December 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.06.005

zbMATH Keywords

comparison theoremboundary value problemparametervariational methoddegree theorymountain pass solutionsub-sup solution method

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Green's functions for ordinary differential equations (34B27) Applications of operator theory to differential and integral equations (47N20) Linear boundary value problems for ordinary differential equations (34B05) Parameter dependent boundary value problems for ordinary differential equations (34B08)

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Existence of solutions for a class of operator equations ⋮ Infinitely many sign-changing solutions for some nonlinear fourth-order beam equations ⋮ Periodic solutions of a class of fourth-order superlinear differential equations ⋮ Third order BVPs with \(\phi\)-Laplacian operators on \([0,+\infty)\) ⋮ Multiple solutions of some boundary value problems with parameters ⋮ Existence of solutions for 2\(m\)th-order periodic boundary value problems ⋮ Existence of solutions for a fourth-order boundary value problem with nonlinear derivative dependence on the half-line via critical point theory

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