Huei-Li Lin

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

We study existence and multiplicity of positive solutions for the following Dirichlet equations: in , on , where is a bounded domain with smooth boundary , , , , , and are continuous functions on which are somewhere positive but which may change sign on .

Multiple positive solutions for a critical elliptic system with concave—convex nonlinearities

We consider a semilinear elliptic system with both concave—convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

Multiple positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in ℝN

AbstractIn this article, we investigate the effect of the coefficient f(z) of the sub-critical nonlinearity. For sufficiently large λ > 0, there are at least k + 1 positive solutions of the semilinear elliptic equations -Δv+λv=f(z)vp-1+h(z)vq-1inℝN;v∈H1(ℝN), where 1 ≤ q < 2 < p < 2* = 2N/(N - 2) for N ≥ 3.AMS (MOS) subject classification: 35J20; 35J25; 35J65.

Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities

By variational methods and some analysis techniques, the multiplicity of positive solutions is obtained for a class of weighted quasilinear elliptic equations with critical Hardy-Sobolev exponents and concave-convex nonlinearities.

MULTIPLE SOLUTIONS FOR SOME NEUMANN PROBLEMS IN EXTERIOR DOMAINS

In this paper, we show that if q ( x ) satisfies suitable conditions, then the Neumann problem -Δ u + u = q ( x )Ⅰ u Ⅰ p −2 u in Ω has at least two solutions of which one is positive and the other changes sign.

Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

We study the existence and multiplicity of positive solutions for the Dirichlet problem where λ > 0, 1 q p = 2* = 2 N /( N − 2), 0 e Ω ⊂ ℝ N , N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on . Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.

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

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation −Δ𝑢

Multiplicity of Positive Solutions for a --Laplacian Type Equation with Critical Nonlinearities

We study the effect of the coefficient of the critical nonlinearity on the number of positive solutions for a --Laplacian equation. Under suitable assumptions for and , we should prove that for sufficiently small , there exist at least positive solutions of the following --Laplacian equation, , where is a bounded smooth domain, , , is the critical Sobolev exponent, and is the -Laplacian of .

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Assume that is a positive continuous function in and satisfies the suitable conditions. We prove that the Dirichlet problem admits at least three positive solutions in an exterior domain.