Uniqueness of Positive Solutions for Some Nonlinear Fourth-Order Equations
نویسندگان
چکیده
منابع مشابه
Periodic Solutions for Some Fully Nonlinear Fourth Order Differential Equations
In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...
متن کاملUniqueness of Positive Solutions to Some Coupled Nonlinear Schrödinger Equations
We study the uniqueness of positive solutions of the following coupled nonlinear Schrödinger equations: ∆u1 − λ1u1 + μ1u1 + βu1u2 = 0 in RN , ∆u2 − λ2u2 + μ2u2 + βu1u2 = 0 in RN , u1 > 0, u2 > 0, u1, u2 ∈ H1(RN ) where N ≤ 3, λ1, λ2, μ1, μ2 are positive constants and β ≥ 0 is a coupling constant. We prove first the uniqueness of positive solution for sufficiently small β > 0. Secondly, ass...
متن کاملExistence and Uniqueness on Periodic Solutions of Fourth-order Nonlinear Differential Equations∗
In this paper, we study the problem of periodic solutions for fourth-order nonlinear differential equations. Under proper conditions, we employ a novel proof to establish some criteria to ensure the existence and uniqueness of T -periodic solutions. Moreover, we give two examples to illustrate the effectiveness of our main results.
متن کاملPositive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations
Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degree theory and cone theory.
متن کاملThe Existence and Uniqueness of Periodic Solutions for Some Nonlinear nth-Order Differential Equations
and Applied Analysis 3 Now, let f̃ : R 1 → R be a continuous function, T -periodic with respect to the first variable, and consider the nth-order differential equation u n f̃ ( t, u, u′, u′′, . . . , u n−1 ) . 2.5 Lemma 2.1 see 14 . Assume that the following conditions hold. i There exists ρ > 0 such that, for each λ ∈ 0, 1 , one has that any possible T -periodic solution u of the problem u n λf̃ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1996
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0247