Concentration of homoclinic solutions for some fourth-order equations with sublinear indefinite nonlinearities
نویسندگان
چکیده
In this paper, we mainly explore the phenomenon of concentration of homoclinic solutions for a class of nonperiodic fourth-order equations with sublinear indefinite nonlinearities. The proof is based on variational methods.
منابع مشابه
A Double Eigenvalue Problem for Schrödinger Equations Involving Sublinear Nonlinearities at Infinity
We present some multiplicity results concerning parameterized Schrödinger type equations which involve nonlinearities with sublinear growth at infinity. Some stability properties of solutions with respect to the parameters are also established in an appropriate Sobolev space.
متن کاملCombined effects of concave-convex nonlinearities and indefinite potential in some elliptic problems
We consider a nonlinear Dirichlet problem driven by the p-Laplacian and a reaction which exhibits the combined effects of concave (that is, sublinear) terms and of convex (that is, superlinear) terms. The concave term is indefinite and the convex term need not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result describing the set of positive solut...
متن کاملHomoclinic Solutions for Fourth Order Traveling Wave Equations
We consider homoclinic solutions of fourth order equations u ′′′′ + βu ′′ + Vu(u) = 0 in R , where V (u) is either the suspension bridge type V (u) = eu − 1 − u or SwiftHohenberg type V (u) = 1 4 (u2 − 1)2. For the suspension bridge type equation, we prove existence of a homoclinic solution for all β ∈ (0, β∗) where β∗ = 0.7427 · · · . For the Swift-Hohenberg type equation, we prove existence o...
متن کاملCompactness of solutions to some geometric fourth-order equations
We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant Q-cur...
متن کاملThe Response of Two-Degree of Freedom Self-Sustained Systems with Quadratic Nonlinearities to a Parametric Excitation (RESEARCH NOTE)
In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 38 شماره
صفحات -
تاریخ انتشار 2014