Solutions of 2\(n\)th Lidstone boundary value problems and dependence on higher order derivatives

DOI10.1016/S0022-247X(03)00011-8zbMath1029.34019OpenAlexW1988875670MaRDI QIDQ1874606

Zhanbing Bai, Weigao Ge

Publication date: 25 May 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(03)00011-8

zbMATH Keywords

maximum principlelower and upper solutionsLidstone boundary value problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Fixed-point theorems (47H10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (31)

Solving singular boundary-value problems of higher even-order ⋮ Positive solutions for 2\(p\)-order and 2\(q\)-order systems of singular boundary value problems with integral boundary conditions ⋮ Existence of nodal solutions for Lidstone eigenvalue problems ⋮ Existence of positive solutions for \(2n\)th-order singular superlinear boundary value problems ⋮ Positive solutions for 2\(n\)th-order singular sub-linear \(m\)-point boundary value problems ⋮ A necessary and sufficient condition for 2\(n\)th-order singular super-linear \(m\)-point boundary value problems ⋮ A class of \(2n\)th-order singular boundary value problems ⋮ On 2nth-order nonlinear multi-point boundary value problems ⋮ The iterative solutions of \(2n\)th-order nonlinear multi-point boundary value problems ⋮ Existence of positive solutions for a system of generalized Lidstone problems ⋮ Unnamed Item ⋮ A necessary and sufficient condition for the existence of symmetric positive solutions of higher-order boundary value problems ⋮ A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problems ⋮ Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives ⋮ Nontrivial solutions for the \(2n^{\text{th}}\) Lidstone boundary value problem ⋮ Existence of positive solutions for singular higher-order differential equations ⋮ Positivity conditions and bounds for Green's functions for higher order two-point BVP ⋮ Existence and uniqueness of positive solutions for a higher order boundary value problem ⋮ Positive solutions for a class of \(2n\)th-order singular boundary value problems ⋮ Existence of positive solutions for higher order \(p\)-Laplacian boundary value problems ⋮ Complementary Lidstone interpolation and boundary value problems ⋮ Collocation for high-order differential equations with Lidstone boundary conditions ⋮ Bifurcation techniques for Lidstone boundary value problems ⋮ Existence of positive solutions for 2\(n\)th-order singular sublinear boundary value problems ⋮ Positive solutions of two-point boundary value problems for 2\(n\)-order differential equations dependent on all derivatives ⋮ Positive solutions of a 2nth-order boundary value problem involving all derivatives via the order reduction method ⋮ Higher-order Lidstone boundary value problems for elliptic partial differential equations ⋮ A fourth-order compact finite difference method for higher-order lidstone boundary value problems ⋮ Global structure of positive solutions for superlinear 2mth-boundary value problems ⋮ On 2\(n\)th-order Lidstone boundary value problems ⋮ Existence of positive solutions of lidstone boundary value problems

Cites Work

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• On fourth order boundary value problems arising in beam analysis
• Existence and uniqueness theorems for fourth-order boundary value problems
• Eigenvalues of Lidstone boundary value problems
• The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems
• The method of lower and upper solutions for fourth-order two-point boundary value problems
• The method of lower and upper solutions for a bending of an elastic beam equation
• General Lidstone problems: Multiplicity and symmetry of solutions
• On positive solutions of some nonlinear fourth-order beam equations
• Fourth order two-point boundary value problems; estimates by two-sided bounds
• Existence for a Fourth-Order Boundary Value Problem under a Two-Parameter Nonresonance Condition

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