Author
Claudianor O. Alves
Other affiliations: Federal University of Paraíba
Bio: Claudianor O. Alves is an academic researcher from Federal University of Campina Grande. The author has contributed to research in topics: Mathematics & Bounded function. The author has an hindex of 38, co-authored 243 publications receiving 4906 citations. Previous affiliations of Claudianor O. Alves include Federal University of Paraíba.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the existence of positive solutions to the class of nonlocal boundary value problems of the type -M(@!"@W|@?u|^2dx)@Du=f(x,u),[email protected],u=0,[email protected][email protected] was studied.
Abstract: This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type -M(@!"@W|@?u|^2dx)@Du=f(x,u),[email protected],u=0,[email protected][email protected], where @W is a smooth bounded domain of @?^N, M is a positive function, and f has subcritical growth.
571 citations
197 citations
TL;DR: In this article, the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type was investigated and a positive solution was found in the case of non-local boundary values.
Abstract: sic) Abstract. This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type
156 citations
TL;DR: In this article, the existence of a positive ground state solution for the following class of elliptic equations was investigated: Δ u + V (x ) u = K ( x ) f ( u ) in R N, where N ⩾ 3, V, K are nonnegative continuous functions and f is a continuous function with a quasicritical growth.
142 citations
TL;DR: In this article, the existence of positive solutions for the following class of nonlocal problems was studied: λ f ( u ) + γ u τ in R N, where τ = 5 for N = 3 and τ ∈ ( 1, + ∞ ) for N= 1, 2, λ is a positive parameter and γ ∈ { 0, 1 }.
Abstract: This paper is concerned with the existence of positive solutions for the following class of nonlocal problem M ( ∫ R N | ∇ u | 2 d x + ∫ R N V ( x ) | u | 2 d x ) [ − Δ u + V ( x ) u ] = λ f ( u ) + γ u τ in R N , where τ = 5 for N = 3 and τ ∈ ( 1 , + ∞ ) for N = 1 , 2 , λ is a positive parameter and γ ∈ { 0 , 1 } . Moreover, M , V , and f are continuous functions satisfying some conditions.
131 citations
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TL;DR: In this paper, the Yang index and critical groups were used to obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems with respect to critical groups.
485 citations
TL;DR: In this article, the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem is studied, where V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term.
460 citations
TL;DR: In this paper, sign changing solutions of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow were obtained for the first time.
377 citations
TL;DR: A survey of the existence and properties of solutions to the Choquard type equations can be found in this paper, where some variants and extensions of its variants can also be found.
Abstract: We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations
$$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$
and some of its variants and extensions.
352 citations
TL;DR: The existence of nontrivial solutions of 4-superlinear Kirchhoff type equations without the P.S. condition was studied in this article. But the existence of sign-changing solutions was not considered.
Abstract: The existence of nontrivial solutions of Kirchhoff type equations is an important nonlocal quasilinear problem; in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4-superlinear Kirchhoff type problems without the P.S. condition, one concerning the existence of a nontrivial solution and the other one concerning the existence of sign-changing solutions and multiple solutions, { − ( a + b ∫ Ω | ∇ u | 2 ) △ u = f ( x , u ) in Ω , u = 0 on ∂ Ω .
331 citations