Tsing-San Hsu

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 solutions for semilinear elliptic equations in unbounded cylinder domains

In this paper, we show that if b ( x ) ≥ b ∞ > 0 in Ω and there exist positive constants C , δ, R 0 such that where x = ( y, z ) ∈ R N with y ∈ R m , z ∈ R n , N = m + n ≥ 3, m ≥ 2, n ≥ 1, 1 p N + 2)/( N − 2), ω ⊆ R m a bounded C 1,1 domain and Ω = ω × R n , then the Dirichlet problem −Δ u + u = b ( x )| u | p −1 u in Ω has a solution that changes sign in Ω, in addition to a positive solution.

Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions

The multiple results of positive solutions for the following quasilinear elliptic equation: −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢

Existence of multiple positive solutions for semilinear elliptic systems involving m critical hardy-sobolev exponents and m sign-changing weight function

Abstract In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS

Abstract In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem - Δ p u - ∑ i = 1 k μ i | u | p - 2 | x - a i | P u = | u | p * - 2 u + λ | u | q - 2 u , x ∈ Ω , where Ω⊂ℝN (N ≥ 3) is a smooth bounded domain such that the different points ai ∈ Ω, i = 1,2,…,k, 0 ≤ μi < μ ¯ = ( N - p p ) p , λ > 0 , 1 ≤ q p , and p * = p N N - p . The results depend crucially on the parameters λ, q and μi for i = 1,2,…,k.

Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Let Ω∋0 be an-open bounded domain in ℝ𝑁(𝑁≥3) and 𝑝∗=(𝑝𝑁/(𝑁−𝑝)). We consider the following quasilinear elliptic system of two equations in 𝑊01,𝑝(Ω)×𝑊01,𝑝(Ω): −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢

MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR ELLIPTIC SYSTEMS WITH CRITICAL SOBOLEV-HARDY AND CONCAVE EXPONENTS ∗

Abstract In this paper, we consider a singular elliptic system with both concave nonlinearities and critical Sobolev-Hardy growth terms in bounded domains. By means of variational methods, the multiplicity of positive solutions to this problem is obtained.

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.