Binlin Zhang

Bio: Binlin Zhang is an academic researcher from Harbin Institute of Technology. The author has contributed to research in topics: Mathematics & p-Laplacian. The author has an hindex of 26, co-authored 61 publications receiving 2142 citations. Previous affiliations of Binlin Zhang include Nankai University & Shandong University of Science and Technology.

Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p -Laplacian in $${\mathbb {R}}^N$$ R N

Abstract: In this paper we investigate the existence of multiple solutions for the nonhomogeneous fractional p-Laplacian equations of Schrodinger–Kirchhoff type $$\begin{aligned} M\left( \iint _{R^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) (-\varDelta )^s_pu+V(x)|u|^{p-2}u=f(x,u)+g(x) \end{aligned}$$ in $${\mathbb {R}}^N$$ , where $$(-\varDelta )^s_p$$ is the fractional p-Laplacian operator, with $$0

Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Abstract: Abstract The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p-Laplacian operator in ℝN. By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers of the weights. Finally, existence of infinitely many pair of entire solutions is obtained by genus theory. Last but not least, the paper covers a main feature of Kirchhoff problems which is the fact that the Kirchhoff function M can be zero at zero. The results of this paper are new even for the standard stationary Kirchhoff equation involving the Laplace operator.

Fractional Kirchhoff problems with critical Trudinger–Moser nonlinearity

Abstract: This paper is concerned with the existence of solutions for a class of fractional Kirchhoff-type problems with Trudinger–Moser nonlinearity: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left( \displaystyle \iint _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^{N/s}}{|x-y|^{2N}}dxdy\right) (-\Delta )^{s}_{N/s}u=f(x,u)\,\, \ &{}\quad \mathrm{in}\ \Omega ,\\ u=0\ \ \ \ &{}\quad \mathrm{in}\ {\mathbb {R}}^N{\setminus } \Omega , \end{array}\right. } \end{aligned}$$ where $$(-\Delta )^{s}_{N/s}$$ is the fractional N / s-Laplacian operator, $$N\ge 1$$ , $$s\in (0,1)$$ , $$\Omega \subset {\mathbb {R}}^N$$ is a bounded domain with Lipschitz boundary, $$M:{\mathbb {R}}^+_0\rightarrow {\mathbb {R}}^+_0$$ is a continuous function, and $$f:\Omega \times {\mathbb {R}}\rightarrow {\mathbb {R}} $$ is a continuous function behaving like $$\exp (\alpha t^{2})$$ as $$t\rightarrow \infty $$ for some $$\alpha >0$$ . We first obtain the existence of a ground state solution with positive energy by using minimax techniques combined with the fractional Trudinger–Moser inequality. Next, the existence of nonnegative solutions with negative energy is established by using Ekeland’s variational principle. The main feature of this paper consists in the presence of a (possibly degenerate) Kirchhoff model, combined with a critical Trudinger–Moser nonlinearity.

A critical fractional Choquard-Kirchhoff problem with magnetic field

Abstract: In this paper, we are interested in a fractional Choquard–Kirchhoff-type problem involving an external magnetic potential and a critical nonlinearity M(∥u∥s,A2)[(−Δ) Asu + u] = λ∫ℝN F(|u|2) |x − y|...

Methods Of Modern Mathematical Physics

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Variational Methods for Nonlocal Fractional Problems

Abstract: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p -Laplacian in $${\mathbb {R}}^N$$ R N

Abstract: In this paper we investigate the existence of multiple solutions for the nonhomogeneous fractional p-Laplacian equations of Schrodinger–Kirchhoff type $$\begin{aligned} M\left( \iint _{R^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) (-\varDelta )^s_pu+V(x)|u|^{p-2}u=f(x,u)+g(x) \end{aligned}$$ in $${\mathbb {R}}^N$$ , where $$(-\varDelta )^s_p$$ is the fractional p-Laplacian operator, with $$0

Nonlinear elliptic equations with variable exponent: Old and new

Abstract: In this survey paper, by using variational methods, we are concerned with the qualitative analysis of solutions to nonlinear elliptic problems of the type { − div A ( x , ∇ u ) = λ | u | q ( x ) − 2 u in Ω u = 0 on ∂ Ω , where Ω is a bounded or an exterior domain of R N and q is a continuous positive function. The results presented in this paper extend several contributions concerning the Lane–Emden equation and we focus on new phenomena which are due to the presence of variable exponents.

Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Abstract: Abstract The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p-Laplacian operator in ℝN. By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers of the weights. Finally, existence of infinitely many pair of entire solutions is obtained by genus theory. Last but not least, the paper covers a main feature of Kirchhoff problems which is the fact that the Kirchhoff function M can be zero at zero. The results of this paper are new even for the standard stationary Kirchhoff equation involving the Laplace operator.