Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains

Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains

“…(3) has at least three positive solutions. Analogous result is stated in [17]. In [10], Cerami and Molle considered the interaction of potentials and the topology of Ω, and also obtained the multiplicity of semilinear elliptic equation with particular form by singular perturbation method.…”

“…Our technique of handling the domain originates from the works concerning about the topological effect of the domain, such as [18,10,9,17]. Using global compactness method, Benci and Cerami [18] investigated the existence of positive solution of the following equation…”

On the existence of positive radial solutions for a certain class of elliptic BVPs

“…Similar problems have been discussed, among others, in [1,8,14,[17][18][19]22] for Ω being an annulus or in [2,11,16,23] for the case when Ω is an exterior domain. Many works of them are devoted to the case, when the right-hand side of the equation has the special form.…”

Positive solutions for sublinear elliptic equations

“…The existence of a nonnegative subsolution (which is neither zero nor positive) was used in [14] to obtain a nonnegative solution; in our approach we obtain a positive one. The problem of symmetry for BVP (4) was studied in the autonomous case in [19], while the multiplicity result was obtained in [12], [16]. Related problems were considered in [15], [17].…”