Results 261 to 270 of about 371,472 (295)

Eigenvalue problems for fourth order differential equations

Annali di Matematica Pura ed Applicata, 1977
This paper is concerned with eigenvalue problems for fourth order differential equations representable by systems of the form: $$x'' + q_{11} (t,\lambda )x + q_{12} (t,\lambda )y = 0, y'' + q_{21} (t,\lambda )x + q_{22} (t,\lambda )y = 0$$ . The boundary conditions are x(a)=y(a)=0=x(b)=y(b) or x(a)=y(a)=0=x′(a)=y′(b).
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Instability results for fourth order differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1980
SYNOPSISIn this paper we give sufficient conditions (Theorems 1 and 2) for the instability of the fourth order differential equation
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Homoclinic solutions for nonlinear general fourth‐order differential equations

Mathematical Methods in the Applied Sciences, 2017
This work provides sufficient conditions for the existence of homoclinic solutions of fourth‐order nonlinear ordinary differential equations. Using Green's functions, we formulate a new modified integral equation that is equivalent to the original nonlinear equation.
Hugo Carrasco, Feliz Minhós
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Asymptotic methods for fourth-order differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1980
SynopsisA new method is developed for obtaining the asymptotic form of solutions of the fourth-order differential equationwherem, nare integers and 1 ≦m,n≦ 2. The method gives new, shorter proofs of the well-known results of Walker in deficiency index theory and covers the cases not considered by Walker.
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A class of fourth order differential equations

Annali di Matematica Pura ed Applicata, 1970
The multiplicity of zeros of solutions of the differential equation $$y^{\left( n \right)} \left( x \right) + p\left( x \right)y\left( x \right) = 0$$ are investigated. On account of the results obtained, a class of fourth order differential equations is defined and the properties of the zeros of the solutions, which vanish in x=a, of a subclass,
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Fourth-order differential equations with logarithmic nonlinearity

São Paulo Journal of Mathematical Sciences
The author investigates a boundary value problem for a differential equation of the fourth order \[ \begin{aligned} &u^{(4)} + Au'' = u\log|u|, \quad \text{ in } (0,1), \\ &u(0) = u''(0) = u(1) = u''(1) = 0, \end{aligned} \] where \(A \in {\mathbb R}\).
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Dirichlet Solutions of Fourth Order Differential Equations

1981
The equation y (4) - (p 1 y′)′ + p 0 y = 0 has exactly two linearly independent solutions on [0,∞) with finite Dirichlet integral. Some applications to the determination of the domains of self - adjoint operators associated with the differential expression and to the minimization of a quadratic functional are discussed.
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ON A FOURTH ORDER SYMMETRIC DIFFERENTIAL EQUATION

The Quarterly Journal of Mathematics, 1982
Paris, R. B., Wood, A. D.
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

Fourth-Order Ordinary Differential Equations

2018
Saad A. Ragab, Hassan E. Fayed
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