Periodic solutions of $x^{\prime \prime } + f(x)x^{\prime 2n} + g(x) = μp(t)$

S. Sędziwy

Displaying similar documents to “Periodic solutions of $x^{''} + f (x) x^{' 2 n} + g (x) = μ p (t)$ ”

Boundedness results of solutions to the equation $x^{\prime\prime\prime}+ax^{\prime\prime}+g(x)x^{\prime}+h(x)=p(t)$ without the hypothesis $h(x)\,\operatorname{sgn}x\geq 0$ for $|x|>R$ .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi $h(x)\,\text{sgn}x\geq 0$ $for|x|>R$ , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

The largest prime factor of X³ + 2

A. J. Irving (2015)

Acta Arithmetica

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Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than $X^{1 + 10^{- 52}}$ .

On the behaviour of solutions of the differential equations ${(r (t) y^{''})}^{'} + q (t) {(y^{'})}^{β} + p (t) y^{α} = f (t)$

N. Parhi, S. Parhi (1986)

Annales Polonici Mathematici

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Periodic solutions to a non-linear parametric differential equation of the third order

Jan Andres, Jan Vorácek (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine $x^{\prime\prime\prime}+a(t,x,x^{\prime},x^{\prime\prime})x^{\prime\prime}+b(t,% x,x^{\prime},x^{\prime\prime})x^{\prime}+h(x)=e(t,x,x^{\prime},x^{\prime\prime})$ con le funzioni $a$ , $b$ , $e$ periodiche in $t$ di periodo $\omega$ .

Boundedness results of solutions to the equation $x^{\prime\prime\prime}+ax^{\prime\prime}+g(x)x^{\prime}+h(x)=p(t)$ without the hypothesis $h(x)\,\text{sgn}x\geq 0$ $for|x|>R$ .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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On the non-convergence of successive approximations in the Darboux problem for the equation $z_{x y}^{''} = f (x, y, z)$

M. Kisielewicz (1977)

Colloquium Mathematicae

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Periodic solutions to a non-linear parametric differential equation of the third order

Jan Andres, Jan Vorácek (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Shifted values of the largest prime factor function and its average value in short intervals

Jean-Marie De Koninck, Imre Kátai (2016)

Colloquium Mathematicae

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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting $s_{q} (n)$ stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence ${(α s_{q} (P (n)))}_{n \in ℕ}$ is uniformly distributed modulo 1.

Periodic solutions of $x " + f (x) x^{' m} + g (x) = 0$

W. R. Utz (1971)

Annales Polonici Mathematici

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Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period

J. W. Heidel (1971)

Annales Polonici Mathematici

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Addenda to “Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period”

J. W. Heidel (1973)

Annales Polonici Mathematici

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$E_{1}$ -degeneration and $d^{'} d^{''}$ -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex $(A, d^{'}, d^{''})$ , we show that if it satisfies the $d^{'} d^{''}$ -lemma and the spectral sequence ${E_{r}^{p, q}}$ induced by $A$ does not degenerate at $E_{0}$ , then it degenerates at $E_{1}$ . We apply this result to prove the degeneration at $E_{1}$ of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of $d^{'} d^{''}$ -lemma.

On hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica $z^{\prime\prime}_{xy}=f(x,y,z,Z^{\prime}_{x},z_{y})$ sul planiquarto $x\geq 0$ , $y\geq 0$ . Qui, $f$ è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza $\alpha$ .

The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian

Jean Mawhin (2006)

Journal of the European Mathematical Society

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We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation $(| u^{'} |^{p - 2} u^{'} {))}^{'} + f (u) u^{'} + g (x, u) = t$ , when $f$ is arbitrary and $g (x, u) \to + \infty$ or $g (x, u) \to - \infty$ when $| u | \to \infty$ . The proof uses upper and lower solutions and the Leray–Schauder degree.

On sets which contain a qth power residue for almost all prime modules

Mariusz Ska/lba (2005)

Colloquium Mathematicae

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A classical theorem of M. Fried [2] asserts that if non-zero integers $β ₁, . . ., β_{l}$ have the property that for each prime number p there exists a quadratic residue $β_{j}$ mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].

Region of variability for spiral-like functions with respect to a boundary point

S. Ponnusamy, A. Vasudevarao, M. Vuorinen (2009)

Colloquium Mathematicae

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For μ ∈ ℂ such that Re μ > 0 let $ℱ_{μ}$ denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and $R e (2 π / μ z f^{'} (z) / f (z) + (1 + z) / (1 - z)) > 0$ in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class $ℱ_{μ} (λ) = f \in ℱ_{μ} : f^{'} (0) = (μ / π) (λ - 1) a n d f^{''} (0) = (μ / π) (a (1 - | λ | ²) + (μ / π) (λ - 1) ² - (1 - λ ²))$ . In the final section we graphically illustrate the region of variability for several sets of parameters.

Products of factorials modulo p

Florian Luca, Pantelimon Stănică (2003)

Colloquium Mathematicae

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We show that if p ≠ 5 is a prime, then the numbers $1 / p (\binom{p}{m ₁, . . ., m_{t}}) | t \geq 1, m_{i} \geq 0 f o r i = 1, . . ., t a n d \sum_{i = 1}^{t} m_{i} = p$ cover all the nonzero residue classes modulo p.

On the nonconvergence of successive approximations in the theory of the equation $z "_{x y} = f (x, y, z, z_{x}^{'}, z_{y}^{'})$

Michał Kisielewicz (1979)

Annales Polonici Mathematici

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Positive solutions for a system of third-order differential equation with multi-point and integral conditions

Rochdi Jebari, Abderrahman Boukricha (2015)

Commentationes Mathematicae Universitatis Carolinae

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This paper concerns the following system of nonlinear third-order boundary value problem: $u_{i}^{'''} (t) + f_{i} (t, u_{1} (t), \dots, u_{n} (t), u_{1}^{'} (t), \dots, u_{n}^{'} (t)) = 0, 0 < t < 1, i \in {1, \dots, n}$ with the following multi-point and integral boundary conditions: $\{\begin{matrix} u_{i} (0) = 0 u_{i}^{'} (0) = 0 u_{i}^{'} (1) = \sum_{j = 1}^{p} β_{j, i} u_{i}^{'} (η_{j, i}) + \int_{0}^{1} h_{i} (u_{1} (s), \dots, u_{n} (s)) d s \end{matrix}$ where $β_{j, i} > 0$ , $0 < η_{1, i} < \dots < η_{p, i} < \frac{1}{2}$ , $f_{i} : [0, 1] \times ℝ^{n} \times ℝ^{n} \to ℝ$ and $h_{i} : [0, 1] \times ℝ^{n} \to ℝ$ are continuous functions for all $i \in {1, \dots, n}$ and $j \in {1, \dots, p}$ . Using Guo-Krasnosel’skii fixed point theorem in cone, we discuss the existence of positive solutions of this problem. We also prove nonexistence of positive solutions and we give some examples to illustrate our results.

On the distribution of prime numbers which are of the form $x^{2} + y^{2} + 1$

Yoichi Motohashi (1970)

Acta Arithmetica

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Displaying similar documents to “Periodic solutions of x ' ' + f ( x ) x ' 2 n + g ( x ) = μ p ( t ) ”

Displaying similar documents to “Periodic solutions of $x^{''} + f (x) x^{' 2 n} + g (x) = μ p (t)$ ”