The Fujita Exponent for Semilinear Heat Equations with Quadratically Decaying Potential

The Fujita Exponent for Semilinear Heat Equations with Quadratically Decaying Potential or in an Exterior Domain

Consider the equation (0.1) ut = ∆u− V u+ au p in R × (0, T ); u(x, 0) = φ(x) 0, in R, where p > 1, n ≥ 2, T ∈ (0,∞], V (x) ∼ ω |x| as |x| → ∞, for some ω 6= 0, and a(x) is on the order |x| as |x| → ∞, for some m ∈ (−∞,∞). A solution to the above equation is called global if T = ∞. Under some additional technical conditions, we calculate a critical exponent p such that global solutions exist fo...

Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

We study the balance between the effect of spatial inhomogeneity of the potential in the dissipative term and the focusing nonlinearity. Sharp critical exponent results will be presented in the case of slow decaying potential.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Local and Global Existence of Solutions to Semilinear Parabolic Initial Value Problems

This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.

Nonhomogeneous Elliptic Equations with Decaying Cylindrical Potential and Critical Exponent

We prove the existence and multiplicity of solutions for a nonhomogeneous elliptic equation involving decaying cylindrical potential and critical exponent.