MULTIPLE SOLUTIONS FOR AN INHOMOGENEOUS SEMILINEAR ELLIPTIC EQUATION IN R N

Multiple solutions for an inhomogeneous semilinear elliptic equation in R

In this paper, we will investigate the existence of multiple solutions for the general inhomogeneous elliptic problem   − u+ u = f (x, u) + μh (x) , x ∈ R , u ∈ H (RN) , (1.1)μ where h ∈ H−1 (RN), N ≥ 2, |f (x, u)| ≤ C1up−1 + C2u with C1 > 0, C2 ∈ [0, 1) being some constants and 2 < p < +∞. ∗Research supported in part by the Natural Science Foundation of China and NSEC †Research supported ...

Multiple solutions and bifurcation of nonhomogeneous semilinear elliptic equations in R N ∗

Tornado Solutions for Semilinear Elliptic Equations in R: Regularity

We give conditions under which bounded solutions to semilinear elliptic equations ∆u = f(u) on domains of R are continuous despite a possible infinite singularity of f(u). The conditions do not require a minimization or variational stability property for the solutions. The results are used in a second paper to show regularity for a familiar class of equations.

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...

Multiple Nontrivial Solutions of Elliptic Semilinear Equations

We find multiple solutions for semilinear boundary value problems when the corresponding functional exhibits local splitting at zero.