Concentration estimates and multiple solutions to elliptic problems at critical growth

By G. Devillanova, S. Solimini. Advances in Differential Equations, 2002

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b18a94df700f6a413d58e77c80d70a724950d5c0

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Citations in the corpus

Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth (2005, methodology): “Just as in the Yamabe-type non-singular framework (i.e., when s = 0), there is no nontrivial solution under global convexity assumption (e.g., when Ω is star-shaped around 0).”
Equations involving fractional Laplacian operator: Compactness and application (2015, methodology): “So we follow the idea in [14] to consider the subcritical problem”
Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent (2012, background): “3) has been studied intensively, and we refer the readers to [12, 13, 15, 17, 32] and references therein.”
Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth (2012, methodology): “Following the idea in [15], we first investigate the following perturbed problem: {− pu = |u|p−2−εu + μ|u|p−2u, x ∈ Ω, u(x) = 0, x ∈ ∂Ω, (1.”
Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case (2015, background): “3) has been studied intensively, and we refer the reader to [12,13,15,18,33] and references therein.”
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential (2010, methodology): “Devillanova and Solimini [13] considered problem (1.1) with μ = 0. They proved the existence of infinitely many solutions for any a > 0. A major step in [ 13 ] to obtain the existence of infinitely many solutions for (1.1) with μ = 0 is to prove that solutions for (1.3), which are bounded in H 1 0 (”
Energy bounds for entire nodal solutions of autonomous superlinear equations (2006, result): “Further existence and multiplicity results were derived in [13–15, 45], whereas the most recent results can be found in [16, 23, 24].”