Exact structure of positive solutions for some 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 کاملExact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity
A p-Laplacian nonlinear elliptic equation with positive and p-superlinear nonlinearity and Dirichlet boundary condition is considered. We first prove the existence of two positive solutions when the spatial domain is symmetric or strictly convex by using a priori estimates and topological degree theory. For the ball domain in RN with N ≥ 4 and the case that 1 < p < 2, we prove that the equation...
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 کاملExistence of positive solutions for boundary value problems of p-Laplacian difference equations
where • N > an integer; • a, c > , and b,d ≥ with ad + ac(N + ) + bc > ; • f and q are continuous and positive; • φp is called p-Laplacian, φp(x) = |x|p–x with p > , its inverse function is denoted by φq(x) with φq(x) = |x|q–x with /p + /q = ; • ∑s i=r x(i) = if r, s ∈ Z and s < r, where Z is the integer set, denote [r, s] = {r, r + , . . . , s} for r, s ∈ Z with r ≤ s. Differen...
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 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: 2005
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.06.058