Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems

On the existence and nonexistence of positive entire large solutions for semilinear elliptic equations

In this paper we are studying the existence of positive entire large solutions for the problem ∆u = p1(x)u α + p2(x)u f(u) in R , N ≥ 3. Moreover, we are interested in the relation between the existence or nonexistence of such solutions for the above problem and the existence or nonexistence of such solutions for the problems ∆u = p1(x)u α and ∆u = p2(x)u f(u).

Existence of Entire Positive Solutions for a Class of Semilinear Elliptic Systems

Under simple conditions on fi and gi, we show the existence of entire positive radial solutions for the semilinear elliptic system ∆u = p(|x|)f1(v)f2(u) ∆v = q(|x|)g1(v)g2(u), where x ∈ RN , N ≥ 3, and p, q are continuous functions.

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate cond...

Existence and Nonexistence of Positive Solutions for Singular Semilinear Elliptic Boundary Value Problems

In this paper we study existence of positive solutions to singular elliptic boundary value problems involving divergence terms in general domains. By constructing suitable upper and lower solutions and making comparison, we obtain suucient conditions for existence and nonexistence of solutions. We also study a concrete example to show that the conditions imposed on parameters appearing in the s...

Existence and Nonexistence of Positive Singular Solutions for Semilinear Elliptic Problems with Applications in Astrophysics