排序方式: 共有9条查询结果,搜索用时 15 毫秒
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We prove the existence of multiple solutions for some systems of second order ODEs with Dirichlet boundary conditions. Such systems are obtained by coupling scalar ODEs with different growth conditions. The proof relies on a global continuation technique. 相似文献
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Alberto Boscaggin Maurizio Garrione 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):825-843
We consider the planar Hamiltonian system $$Ju^{\prime} = \nabla F(u) + \nabla_u R(t,u), \quad t \in [0,T], \,u \in \mathbb{R}^2,$$ with F(u) positive and positively 2-homogeneous and ${\nabla_{u}R(t, u)}$ sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well. 相似文献
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Alberto Boscaggin Maurizio Garrione 《Journal of Dynamics and Differential Equations》2016,28(1):167-187
We study the Neumann boundary value problem for the second order ODE where \(g \in {\mathcal {C}}^1({\mathbb {R}})\) is a bounded function of constant sign, \(a^+,a^-: [0,T] \rightarrow {\mathbb {R}}^+\) are the positive/negative part of a sign-changing weight \(a(t)\) and \(\mu > 0\) is a real parameter. Depending on the sign of \(g^{\prime }(u)\) at infinity, we find existence/multiplicity of solutions for \(\mu \) in a “small” interval near the value The proof exploits a change of variables, transforming the sign-indefinite Eq. (1) into a forced perturbation of an autonomous planar system, and a shooting argument. Nonexistence results for \(\mu \rightarrow 0^+\) and \(\mu \rightarrow +\infty \) are given, as well.
相似文献
$$\begin{aligned} u^{\prime \prime } + (a^+(t)-\mu a^-(t))g(u) = 0, \qquad t \in [0,T], \end{aligned}$$
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$$\begin{aligned} \mu _c = \frac{\int _0^T a^+(t) \, dt}{\int _0^T a^-(t) \, dt}\,. \end{aligned}$$
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Alberto Boscaggin Alessandro Fonda Maurizio Garrione 《Nonlinear Analysis: Theory, Methods & Applications》2012
By the use of the Poincaré–Birkhoff fixed point theorem, we prove a multiplicity result for periodic solutions of a second order differential equation, where the nonlinearity exhibits a singularity of repulsive type at the origin and has linear growth at infinity. Our main theorem is related to previous results by Rebelo (1996, 1997) and and Rebelo and Zanolin (1996) and , in connection with a problem raised by del Pino et al. (1992) [1]. 相似文献
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We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODE where is a positive function on , superlinear at zero and sublinear at infinity, and is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided. 相似文献
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Alberto Boscaggin Maurizio Garrione 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):4166-4185
In the general setting of a planar first order system
(0.1) 相似文献
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Using the Poincaré–Birkhoff fixed point theorem, we prove that for every β > 0 and for a large (both in the sense of prevalence and of category) set of continuous and T-periodic functions \({f: \mathbb{R} \to \mathbb{R}}\) with \({\int_0^T f(t)\,dt = 0}\) , the forced pendulum equation $$x'' + \beta \sin x = f(t) $$ has a subharmonic solution of order k for every large integer number k. This improves the well known result obtained with variational methods, where the existence when k is a (large) prime number is ensured. 相似文献
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