Nontrivial solutions of singular fourth-order Sturm–Liouville boundary value problems with a sign-changing nonlinear term

2011 ◽  
Vol 217 (15) ◽  
pp. 6700-6708 ◽  
Author(s):  
Wenxi Fan ◽  
Xinan Hao ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nontrivial Solutions ◽  
Sturm Liouville

scholarly journals Existence of Nontrivial Solutions for Unilaterally Asymptotically Linear Three-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongyu Li
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Lattice Structure ◽  
Boundary Value ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Asymptotically Linear ◽  
Sign Changing Solutions ◽  
Ordered Banach Spaces

Using fixed point theorems in ordered Banach spaces with the lattice structure, we consider the existence of nontrivial solutions under the condition that the nonlinear term can change sign and study the existence of sign-changing solutions for some second order three-point boundary value problems. Our results improve and generalize on those in the literatures.

scholarly journals On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order

2021 ◽  
Author(s):  
A. A. Vladimirov ◽  
A. A. Shkalikov
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Nontrivial Solutions ◽  
New Approach ◽  
Oscillatory Problem ◽  
Derivatives Of ◽  
Inertia Index ◽  
Oscillation Properties

Abstract The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is studied. We specify the types of problems for which such a connection can be established. In addition, we specify the types of problems for which a connection between the inertia index and the number of internal zeros of the derivatives of nontrivial solutions can be established. Examples demonstrating the effectiveness of the proposed new approach to an oscillatory problem are considered.

scholarly journals Existence and Nonexistence of Solutions for Fourth-Order Nonlinear Difference Boundary Value Problems via Variational Methods

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Variational Methods ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Nontrivial Solutions ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions

This paper is concerned with boundary value problems for a fourth-order nonlinear difference equation. Via variational methods and critical point theory, sufficient conditions are obtained for the existence of at least two nontrivial solutions, the existence ofndistinct pairs of nontrivial solutions, and nonexistence of solutions. Some examples are provided to show the effectiveness of the main results.

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