Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods
نویسندگان
چکیده
منابع مشابه
Nontrivial solutions for p-Laplacian systems
The paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div (|∇ui |p−2∇ui)+ λfi(u1, . . . , un)= 0 in Ω, ui = 0 on ∂Ω, i = 1, . . . , n, where p > 1, Ω is a bounded domain in RN (N 2) with smooth boundary, and fi , i = 1, . . . , n, are continuous, nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1 |ui |, we prove t...
متن کاملThe Extremal Solution for the Fractional Laplacian
We study the extremal solution for the problem (−∆)u = λf(u) in Ω, u ≡ 0 in R \ Ω, where λ > 0 is a parameter and s ∈ (0, 1). We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded in dimensions n < 4s. We also show that, for exponential and power-like ...
متن کاملEigenvalue of Fractional Differential Equations with p-Laplacian Operator
Differential equations of fractional order have been recently proved to be valuable tools in the modeling of many phenomena arising from science and engineering, such as viscoelasticity, electrochemistry, control, porous media, and electromagnetism. For detail, see the monographs of Kilbas et al. [1],Miller and Ross [2], and Podlubny [3] and the papers [4–23] and the references therein. In [16]...
متن کاملNontrivial Solutions of p-Superlinear p-Laplacian Problems via a Cohomological Local Splitting
We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.
متن کاملContinuity results with respect to domain perturbation for the fractional p-Laplacian
In this paper we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p−laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.
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: Advances in Mathematical Physics
سال: 2017
ISSN: 1687-9120,1687-9139
DOI: 10.1155/2017/5317213