Blow up Points of Solution Curves for a Semilinear Problem
نویسندگان
چکیده
We study a semilinear elliptic equation with an asymptotic linear nonlinearity. Exact multiplicity of solutions are obtained under various conditions on the nonlinearity and the spectrum set. Our method combines a bifurcation approach and Leray–Schauder degree theory.
منابع مشابه
Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions
We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut uxx − a x, t f u , 0 < x < 1, t ∈ 0, T , with boundary conditions ux 0, t 0, ux 1, t b t g u 1, t , blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-u...
متن کاملExistence and classification of characteristic points at blow-up for a semilinear wave equation
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ R the set of all characteristic points and show that S has an empty interior. Finally, given x0 ∈ S, we show that in self...
متن کاملBLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM
In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملExistence and characterization of characteristic points for a semilinear wave equation in one space dimension
Abstract: We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ the set of all characteristic points, and show that the S has an empty interior. Finally, given x0 ∈ S, we show...
متن کامل