Positive or sign-changing solutions for a critical semilinear nonlocal equation

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Blow up of Solutions with Positive Initial Energy for the Nonlocal Semilinear Heat Equation

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

Multiple Positive Solutions for Semilinear Elliptic Equations with Sign - Changing Weight Functions

and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...

Asymptotic behaviour for a semilinear nonlocal equation

We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...