Nonexistence of global solutions of a quasilinear hyperbolic equation
نویسندگان
چکیده
منابع مشابه
Nonexistence of Global Solutions of a Nonlinear Hyperbolic System
Consider the initial value problem utt = ∆u+ |v|p, vtt = ∆v + |u|q, x ∈ Rn, t > 0, u(x, 0) = f(x), v(x, 0) = h(x), ut(x, 0) = g(x), vt(x, 0) = k(x), with 1 ≤ n ≤ 3 and p, q > 0. We show that there exists a bound B(n) (≤ ∞) such that if 1 < pq < B(n) all nontrivial solutions with compact support blow up in finite time.
متن کاملResonance for Quasilinear Hyperbolic Equation
git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...
متن کاملExistence and Nonexistence of Positive Radial Solutions for Quasilinear Systems
The paper deals with the existence and nonexistence of positive radial solutions for the weakly coupled quasilinear system div (
متن کاملExistence and Nonexistence of Positive Solutions for Quasilinear Systems
The paper deals with the existence and nonexistence of positive solutions for a class of p-Laplacian systems. We investigate the effect of the size of the domain on the existence of positive solution for the problem in sublinear cases. We will use fixed point theorems in a cone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted...
متن کاملPositive solutions for a quasilinear Schrödinger equation
We consider the quasilinear problem −εpdiv(|∇u|p−2∇u) + V (z)up−1 = f(u) + up−1, u ∈W (R ), where ε > 0 is a small parameter, 1 < p < N , p∗ = Np/(N − p), V is a positive potential and f is a superlinear function. Under a local condition for V we relate the number of positive solutions with the topology of the set where V attains its minimum. In the proof we apply Ljusternik-Schnirelmann theory...
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: Mathematical Inequalities & Applications
سال: 1998
ISSN: 1331-4343
DOI: 10.7153/mia-01-35