Multiple solutions for elliptic problems with singular and sublinear potentials

Abstract

Abstract. For certain positive numbers µ and λ, we establish the multiplicity of solutions to the problemwhere Ω is a bounded open domain in R N (N ≥ 3) containing the origin with smooth boundary ∂Ω, while f : R → R is continuous, superlinear at zero and sublinear at infinity.

Three solutions for a Navier boundary value problem involving the -biharmonic

“…Thanks to (i 3 ), for each λ > 0, one has lim u →∞ (Φ(u) + λΨ (u)) = +∞, (12) and so the assumption (5) of Theorem A holds. Now, put…”

“…In recent years, many papers [3][4][5][6][7][8][9][10][11][12][13][14][15][16]26] have appeared, in which the technical approach adopted is based on the three-critical-points theorem obtained by Ricceri [17]. In [3,6,[8][9][10], the authors, by using Ricceri's three-critical-points theorem [17], obtained the existence of at least three weak solutions to the Dirichlet boundary value problem.…”

Existence of two weak solutions for some singular elliptic problems

“…For completeness, we recall that a careful and interesting analysis of singular elliptic problems was developed in the monographs [16,22] as well as the papers [10,15,[17][18][19] and references therein.…”

Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

“…Recently, using Bonanno's three critical point theorem [2], Kristály and Varga [6] have obtained the existence of multiple weak solutions to the problem…”