A class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$

Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights

Recommended by Pavel Drabek We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu − μ/|x| 2 u λfx|u| q−2 u gx|u| 2 * −2 u in Ω, u 0 on ∂Ω, where 0 ∈ Ω ⊂ R N N ≥ 3 is a bounded domain with smooth boundary ∂Ω, λ > 0, 0 ≤ μ < μ N − 2 2 /4, 2 * 2N/N − 2, 1 ≤ q < 2, and f, g are continuous functions on Ω which are somewhere positive but which may change...

Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms

where Ω ⊂ R is a smooth domain with smooth boundary ∂Ω such that 0 Î Ω, Δpu = div(|∇u|∇u), 1 < p < N, μ < μ̄ = ( N−p p ), l >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on ̄, μ̄ = ( N−p p ) p is the best Hardy constant and p∗ = Np N−p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solu...

Multiplicity of solutions for a class of quasilinear elliptic equations with concave and convex terms in R ∗

In this paper the Fountain theorem is employed to establish infinitely many solutions for the class of quasilinear Schrödinger equations −Lpu + V (x)|u|p−2u = λ|u|q−2u + μ|u|r−2u in R, where Lpu = (|u′|p−2u′)′ + (|(u2)′|p−2(u2)′)′u, λ, μ are real parameters, 1 < p <∞, 1 < q < p, r > 2p and the potential V (x) is nonnegative and satisfies a suitable integrability condition. AMS Subject Classific...

Existence of Infinitely Many Large Solutions for a Class of Fourth - Order Elliptic Equations In

Multiple Positive Solutions for Semilinear Elliptic Equations in RN Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫