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

On positive solutions for a class of nonlocal problems

In this paper, we study a class of nonlocal semilinear elliptic problems with inhomogeneous strong Allee effect. By means of variational approach, we prove that the problem has at least two positive solutions for large λ under suitable hypotheses about nonlinearity. We also prove some nonexistence results. In particular, we give a positive answer to the conjecture of Liu-Wang-Shi.

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

Existence and Multiplicity of Positive Solutions to a Quasilinear Elliptic Equation with Strong Allee Effect Growth Rate

In this paper we consider a p-Laplacian equation with strong Allee effect growth rate and Dirichlet boundary condition { div(|∇u|p−2∇u) + λf(x, u) = 0, x ∈ Ω, u = 0, x ∈ ∂Ω, (Pλ) where Ω is a bounded smooth domain in R for N ≥ 1, p > 1, and λ is a positive parameter. By using variational methods and a suitable truncation technique, we prove that problem (Pλ) has at least two positive solutions ...

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