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A class of fourth order differential equations
Annali di Matematica Pura ed Applicata, 1970The 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 SciencesThe 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
1981The 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, 1982Paris, R. B., Wood, A. D.
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Existence of homoclinic solutions for a fourth order differential equation with a parameter
Applied Mathematics and Computation, 2015Tie-xiang Li +2 more
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Fourth-Order Ordinary Differential Equations
2018Saad A. Ragab, Hassan E. Fayed
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