Positive solutions for parametric $p$-Laplacian equations
نویسندگان
چکیده
منابع مشابه
On positive solutions of p-Laplacian-type equations
Let Ω be a domain in Rd, d ≥ 2, and 1 < p < ∞. Fix V ∈ Lloc(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by Q(u) := 1 p ∫ Ω (|∇u|+V |u|)dx, Q(u) :=−∇· (|∇u|∇u)+V |u|u. In this paper we discuss several aspects of relations between functionalanalytic properties of the functional Q and properties of positive solutions of the equation Q′(u) = 0. 2000 Mathematics Subject Classif...
متن کاملPositive radial solutions for p-Laplacian systems
The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1...
متن کاملPositive decaying solutions for differential equations with phi-Laplacian
*Correspondence: [email protected] 1Faculty of Science, Masaryk University Brno, Kotlářská 2, Brno, 611 37, The Czech Republic Full list of author information is available at the end of the article Abstract We solve a nonlocal boundary value problem on the half-close interval [1,∞) associated to the differential equation (a(t)|x′|α sgn x′)′ + b(t)|x|β sgn x = 0, in the superlinear case α < β ....
متن کاملPositive Solutions of Three-point Boundary-value Problems for P-laplacian Singular Differential Equations
In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem −[φp(u)] = q(t)f(t, u(t)), 0 < t < 1 subject to u(0)− g(u′(0)) = 0, u(1)− βu(η) = 0 or to u(0)− αu(η) = 0, u(1) + g(u′(1)) = 0, where φp is the p-Laplacian operator, 0 < η < 1; 0 < α, β < 1 are fixed points and g is a monotone continuous function defined on the real line R with g(0) = ...
متن کاملThree Positive Solutions for P-laplacian Functional Dynamic Equations on Time Scales
In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, [Φp(u ∆(t))]∇ + a(t)f(u(t), u(μ(t))) = 0, t ∈ (0, T )T, u0(t) = φ(t), t ∈ [−r, 0]T, u(0)−B0(u(η)) = 0, u(T ) = 0, . using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result.
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: Communications on Pure and Applied Analysis
سال: 2016
ISSN: 1534-0392
DOI: 10.3934/cpaa.2016002