Multiple solutions for an elliptic system near resonance

Multiple Solutions For Semilinear Elliptic Boundary Value Problems At Resonance

In recent years several nonlinear techniques have been very successful in proving the existence of weak solutions for semilinear elliptic boundary value problems at resonance. One technique involves a variational approach where solutions are characterized as saddle points for a related functional. This argument requires that the Palais-Smale condition and some coercivity conditions are satisfie...

Multiple Solutions for a Singular Quasilinear Elliptic System

We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* ...

POSITIVE SOLUTIONS AND MULTIPLE SOLUTIONS AT NON-RESONANCE, RESONANCE AND NEAR RESONANCE FOR HEMIVARIATIONAL INEQUALITIES WITH p-LAPLACIAN

In this paper we study eigenvalue problems for hemivariational inequalities driven by the p-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative p-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and ...

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 for an Elliptic Problem Related to Vortex Pairs