A Class of --Laplacian Type Equation with Potentials Eigenvalue Problem in
Mingzhu Wu,Zuodong Yang +1 more
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TLDR
The nonlinear elliptic eigenvalue problem is studied in this paper, where the key ingredient is a special constrained minimization method, which is the same as in this paper.Abstract:
The nonlinear elliptic eigenvalue problem
, where
and
are studied. The key ingredient is a special constrained minimization method.read more
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Existence of positive solutions for a class of p&q elliptic problems with critical growth on RN
TL;DR: In this paper, the existence of positive solutions to the class of p & q elliptic problems with critical growth type − div (a ( ∇ u | p ) + b ( | u| p ) | p − 2 u = λ f ( u ) + | u | γ ⁎ −2 u, u ( z ) > 0, ∀ x ∈ R N, where λ is a positive parameter, a : R → R is a function of C 1 class and b, f : R→ R are continuous functions.
Journal ArticleDOI
Generalized eigenvalue problems for (p,q)-Laplacian with indefinite weight
TL;DR: In this article, the existence and non-existence results on a positive solution for quasilinear elliptic equations of the form − Δ r u − μ Δ r ⁎ u = λ m r (x ) | u | r − 2 u in Ω with 1 r ≠ r ∞ and μ > 0, under Dirichlet boundary condition, where Ω is a bounded domain in R N and m r is a weight function in L ∞ ( Ω ) admitting sign-change.
Journal ArticleDOI
Multiplicity of positive solutions to a p–q-Laplacian equation involving critical nonlinearity
Honghui Yin,Zuodong Yang +1 more
TL;DR: In this paper, the existence of multiple solutions of a p − q -Laplacian equation with convex and Sobolev critical nonlinearity was established by some standard variational methods, whose key is to construct homotopies between Ω and levels of the functional I θ.
Journal ArticleDOI
Existence of least energy positive, negative and nodal solutions for a class of p&q-problems with potentials vanishing at infinity
TL;DR: In this paper, the authors proved the existence of at least three nontrivial solutions for the class of p & q problems given by − div ( a ( ∇ u | p ) | ∇u | p − 2 u ) + V ( x ) b ( | u |p ) | u| p− 2 u = K (x ) f ( u ), in R N, where N ≥ 3, 2 ≤ p N, a, b, f are C 1 real functions and V, K are positive and continuous functions.
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A class of p-q-Laplacian type equation with concave-convex nonlinearities in bounded domain
Honghui Yin,Zuodong Yang +1 more
TL;DR: In this paper, the existence of multiple solutions of a class of p-q -Laplacian equation involving concave-convex nonlinearities was established. And the existence results of solutions were obtained by variational methods, such that for every θ ∈ ( 0, θ ⁎ ), the above problem possesses infinitely many weak solutions.
References
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Nonlinear scalar field equations, I existence of a ground state
TL;DR: In this article, a constrained minimization method was proposed for the case of dimension N = 1 (Necessary and sufficient conditions) for the zero mass case, where N is the number of dimensions in the dimension N.
Journal ArticleDOI
Nonlinear scalar field equations, II existence of infinitely many solutions
Journal ArticleDOI
On the Existence of Positive Entire Solutions of a Semilinear Elliptic Equation
TL;DR: In this paper, the existence of positive solutions of the above equation in a ball with the boundary condition u = 0 has been studied under suitable hypotheses under radially symmetric potentials.
Journal ArticleDOI
Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations
Jaeyoung Byeon,Zhi-Qiang Wang +1 more
TL;DR: In this paper, the existence and qualitative properties of standing wave solutions for the nonlinear Schrodinger equation with E being a critical frequency in the sense that the amplitude goes to 0.
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