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1.
Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented. 相似文献
2.
The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit. 相似文献
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In this paper, we mainly explore the phenomenon of concentration of homoclinic solutions for a class of nonperiodic fourth-order equations with sublinear indefinite nonlinearities. The proof is based on variational methods. 相似文献
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Non-destructive testing of tubes using a time reverse numerical simulation (TRNS) method 总被引:4,自引:0,他引:4
A method for the detection of defects in cylindrical structures and the determination of their positions and orientations is presented in this paper. The scattered field, which is generated by the interaction of excited guided waves with a defect, is evaluated with an approach named time reverse numerical simulation method (TRNS). Since the excited waves and the scattered field propagate along the sample, the time-consuming scanning of the whole tube can be eliminated. The scattered displacement field is measured in three dimensions over time with a laser vibrometer at different locations distributed equally around the circumference at a fixed axial coordinate far away from the defect. Instead of analyzing the complicated time signals directly, they are played back in time. If the recorded displacement histories of the scattered field are reversed in time and played back in an identical structure, the waves travel back the same path and interfere to a maximum at their origin. The result is an amplitude increase at the position of the defect where the scattered field was generated. Instead of playing back the recorded time signals in an experiment, this step is replaced by a numerical simulation. Only this enables the visualization and detection of the amplitude increase. As long as the simulation is of high accuracy, the position of the maximum interference corresponds exactly to the location of the defect in the experiment, although no defect is implemented in the simulation. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(3):520-529
Recent protein observations motivate the dark-soliton study to explain the energy transfer in the proteins. In this paper we will investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. Painlevé analysis is performed to prove the equation is integrable. Through the introduction of an auxiliary function, bilinear forms and dark N-soliton solutions are constructed with the Hirota method and symbolic computation. Asymptotic analysis on the two-soliton solutions indicates that the soliton collisions are elastic. Decrease of the coefficient of higher-order effects can increase the soliton velocities. Graphical analysis on the two-soliton solutions indicates that the head-on collision between the two solitons, overtaking collision between the two solitons and collision between a moving soliton and a stationary one are all elastic. Collisions among the three solitons are all pairwise elastic. 相似文献
9.
Qingqu Zhuang 《Applied mathematics and computation》2011,218(7):3587-3595
A Legendre-Galerkin spectral-element method is proposed to solve the one-dimensional fourth-order equations. C1-continuity between the elemental-faces is imposed by constructing appropriate basis functions. The method leads to linear systems with sparse matrices for the discrete variational formulations. Rigorous error analysis is carried out to establish the convergence of the method. Several numerical examples are provided to confirm the theoretical results. 相似文献
10.
Multiple solutions for fourth-order boundary value problem 总被引:4,自引:0,他引:4
In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions. 相似文献