Harmonic and Nonperiodic Solutions of Velocity-Dependent Conservative Equations

Counting solutions of perturbed harmonic map equations

In this paper we consider perturbed harmonic map equations for maps between closed Riemannian manifolds. In the case where the target manifold has negative sectional curvature we prove among other results that for a large class of semilinear and quasilinear perturbations, the perturbed harmonic map equations have solutions in any homotopy class of maps for which the Euler characteristic of the ...

Lindstedt Series for Periodic Solutions of Beam Equations with Quadratic and Velocity Dependent Nonlinearities

Abstract. We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Dirichlet boundary conditions. Such nonlinear PDE can be regarded as a simple model describing oscillations of flexible structures like suspension bridges in presence of an unifo...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Generic Regularity of Conservative Solutions to Camassa-Holm Type Equations

This paper mainly proves the generic properties of the Camassa-Holm equation and the two-component Camassa-Holm equation by Thom’s transversality Lemma. We reveal their differences in generic regularity and singular behavior.

Boundary singularities of solutions of N-harmonic equations with absorption