An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.

Spradlin, Gregory S.

Displaying similar documents to “An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.”

Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in $ℝ^{N}$ .

Hsu, Tsing-San (2010)

Boundary Value Problems [electronic only]

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Multiplicity results for positive solutions to non-autonomous elliptic problems.

Qiao, Ning, Wang, Zhi-Qiang (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Weak linking theorems and Schrödinger equations with critical Sobolev exponent

Martin Schechter, Wenming Zou (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation $- Δ u + V (x) u = {K (x) | u |}^{2^{*} - 2} u + g (x, u), u \in W^{1, 2} (𝐑^{N})$ , where $N \geq 4; V, K, g$ are periodic in $x_{j}$ for $1 \leq j \leq N$ and 0 is in a gap of the spectrum of $- Δ + V$ ; $K > 0$ . If $0 < g (x, u) u \leq {c | u |}^{2^{*}}$ for an appropriate constant $c$ , we show that this equation has a nontrivial solution.

Interior estimates for some semilinear elliptic problem with critical nonlinearity

Pierpaolo Esposito (2007)

Annales de l'I.H.P. Analyse non linéaire

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Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator.

Garcia-Huidobro, Marta, Manasevich, Raul, Ubilla, Pedro (1995)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Multiple solutions to some singular nonlinear Schrödinger equations.

Lazzo, Monica (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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The fixed point property in a Banach space isomorphic to $c_{0}$

Costas Poulios (2014)

Commentationes Mathematicae Universitatis Carolinae

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We consider a Banach space, which comes naturally from $c_{0}$ and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets.

Ground states of nonlinear Schrödinger equations with potentials

Yongqing Li, Zhi-Qiang Wang, Jing Zeng (2006)

Annales de l'I.H.P. Analyse non linéaire

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