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Sharp Condition for Global Existence of Supercritical Nonlinear Schrödinger Equation with a Partial Confinement
We study the L 2 -supercritical nonlinear Schrödinger equation (NLS) with a partial confinement, which is the limit case of the cigar-shaped model in...
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Existence of Three Solutions to a Class of Nonlinear Equations on Graphs
Let u be a function on locally finite connect graph G = ( V, E ) and Ω be a bounded subset of V . We consider the nonlinear Dirichlet boundary condition...
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Ground state solutions for quasilinear Schrödinger equations with critical Berestycki–Lions nonlinearities
We consider the quasilinear Schrödinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the...
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On Chien’s question to the Hu-Washizu three-field functional and variational principle
There is an open question, namely Chien’s question, in construction of a generalized functional in elasticity, i.e., why the stress-strain relation...
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Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term
In this paper, a class of Kirchhoff type equations in ℝ N ( N ⩾ 3) with zero mass and a critical term is studied. Under some appropriate conditions,...
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Existence of Solutions for the Laplacian Equation with Exponential Neumann Boundary Condition
In this paper, we consider the Laplacian equation with exponential Neumann boundary condition on a compact Riemann surface Σ with nonempty boundary ∂ Σ...
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Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of...
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Hopf bifurcation of a tumor immune model with time delay
In this paper, a tumor immune model with time delay is studied. First, the stability of nonnegative equilibria is analyzed. Then the time delay τ is...
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Estimates for Extremal Values for a Critical Fractional Equation with Concave-Convex Nonlinearities
In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set...
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Multiple Positive Solutions to a Class of Modified Nonlinear Schrödinger Equation in a High Dimension
The existence and multiplicity of positive solutions for equation (1.1) with the new critical exponent 4 < p < 2·2* shall be investigated in a high...
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Existence Results for Singular Fractional p-Kirchhoff Problems
This paper is concerned with the existence and multiplicity of solutions for singular Kirchhoff-type problems involving the fractional p -Laplacian...
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Anisotropic Moser–Trudinger Inequality Involving Ln Norm in the Entire Space ℝn
Let F : ℝ n → [0, + ∞) be a convex function of class C 2 (ℝ n {0}) which is even and positively homogeneous of degree 1, and its polar F 0 represents a...
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains
In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p -Laplace operator...