A strong comparison principle for the $p$-Laplacian
نویسندگان
چکیده
منابع مشابه
A STRONG COMPARISON PRINCIPLE FOR THE p-LAPLACIAN
We consider weak solutions of the differential inequality of pLaplacian type −∆pu− f(u) ≤ −∆pv − f(v) such that u ≤ v on a smooth bounded domain in RN and either u or v is a weak solution of the corresponding Dirichlet problem with zero boundary condition. Assuming that u < v on the boundary of the domain we prove that u < v, and assuming that u ≡ v ≡ 0 on the boundary of the domain we prove u ...
متن کاملCOMPARISON PRINCIPLE AND CONSTRAINED RADIAL SYMMETRY FOR THE SUBDIFFUSIVE p-LAPLACIAN
A comparison principle for the subdiffusive p-Laplacian in a possibly nonsmooth and unbounded open set is proved. The result requires that the involved sub and supersolution are positive, and the ratio of the former to the latter is bounded. As an application, constrained radial symmetry for overdetermined problems is obtained. More precisely, both Dirichlet and Neumann conditions are prescribe...
متن کاملA Note on Strong Resonance Problems for P-laplacian
In this note, we study the existence of the weak solutions for the p-Laplacian with strong resonance, which generalizes the previous results in one-dimension.
متن کاملSTRONG RESONANCE PROBLEMS FOR THE ONE-DIMENSIONAL p-LAPLACIAN
We study the existence of the weak solution of the nonlinear boundary-value problem −(|u′|p−2u′)′ = λ|u|p−2u+ g(u)− h(x) in (0, π), u(0) = u(π) = 0 , where p and λ are real numbers, p > 1, h ∈ Lp (0, π) (p′ = p p−1 ) and the nonlinearity g : R → R is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of...
متن کاملOn a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian and its applications
We present a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian, which is an extension of the classic identity for the ordinary Laplace. Also, some applications of our results in Sobolev spaces with variable exponent are suggested.
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: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-08847-8