Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Infinitely Many Solutions of Superlinear Elliptic Equation

and Applied Analysis 3 Lemma 6 (see [17]). Assume that |Ω| < ∞, 1 ≤ p, r ≤ ∞, f ∈ C(Ω×R), and |f(x, u)| ≤ c(1+|u|). Then for every

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

Weakly and strongly singular solutions of semilinear fractional elliptic equations

If p ∈ (0, N N−2α ), α ∈ (0, 1), k > 0 and Ω ⊂ R is a bounded C domain containing 0 and δ0 is the Dirac measure at 0, we prove that the weak solution of (E)k (−∆) u + u = kδ0 in Ω which vanishes in Ω is a weak singular solution of (E)∞ (−∆) u + u = 0 in Ω \ {0} with the same outer data. Furthermore, we study the limit of weak solutions of (E)k when k → ∞. For p ∈ (0, 1+ 2α N ], the limit is inf...