Mixed Local and Nonlocal Dirichlet (p, q)-Eigenvalue Problem
نویسندگان
چکیده
We consider the spectral problem for mixed local and nonlocal p-Laplace operator. discuss existence regularity of eigenfunction associated Dirichlet (p, q)-eigenvalue in a bounded domain Ω ⊂ ℝN under assumption that 1 < p ∞ q p∗ where = Np/(N − p) if N ⩾ N.
منابع مشابه
On a Nonlocal Eigenvalue Problem
We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in some reaction-diiusion systems. We give some suucient (and explicit) conditions for the stability in the general case.
متن کاملThe Study of a Nonlocal Eigenvalue Problem
We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for the Sel'kov model, the Gray-Scott system and angiogenesis. We give some suucient and explicit conditions for stability.
متن کاملThe Ratio of Eigenvalues of the Dirichlet Eigenvalue Problem for Equations with One-Dimensional p-Laplacian
and Applied Analysis 3 and using 1.9 we have ( tanpt )′ 1 − sinpt ( cospt )′ cospt 1 ∣ ∣tanpt ∣ ∣. 1.10 Like for p 2, tanpt > t for t ∈ 0, πp/2 and tanpt < t for t ∈ −πp/2, 0 , which is equivalent to ∣ ∣sinp ∣ ∣p > tΦ ( sinpt ) cospt 1.11 for t ∈ −πp/2, πp/2 , t / 0. A similar formula to 1.10 for cotp is related to the Riccati equation associated with 1.1 . Namely, if x t / 0 is a solution of 1...
متن کاملThe Dirichlet problem for some nonlocal diffusion equations
We study the Dirichlet problem for the non-local diffusion equation ut = ∫ {u(x+ z, t)− u(x, t)} dμ(z), where μ is a L function and “u = φ on ∂Ω× (0,∞)” has to be understood in a non-classical sense. We prove existence and uniqueness results of solutions in this setting. Moreover, we prove that our solutions coincide with those obtained through the standard “vanishing viscosity method”, but sho...
متن کاملThe p - Laplace eigenvalue problem as p → ∞ in a
We consider the p–Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p → ∞.
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 Sciences
سال: 2023
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-023-06389-y