Existence of a positive solution to Kirchhoff type problems without compactness conditions

By Yuhua Li, Fuyi Li, Junping Shi. 2012

378 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0059085a73647b3a12b460e3efd6ae23f523ad77

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

The critical problem of Kirchhoff type elliptic equations in dimension four (2014, background): “In recent years, the analysis of the stationary problems of (P0) has been extensively carrying out by many authors, see [2][3][4][10][11][16][17][18][20][21] [22][26][28][29] and so on.”
Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in $R^3$ (2013, methodology): “To overcome this difficulty, inspired by [21, 36], we use an indirect approach developed by Jeanjean.”
Existence of positive solutions to Kirchhoff type problems with zero mass (2014, neutral): “As in [17], we prove in this paper the existence of positive solutions to (1.”
Existence of solution for a class of nonlocal elliptic problem via sub-supersolution method (2013, background): “More details about this class of problem can be see in [4], [5], [7], [16], [20] and [21] and their references.”
Study of a nonlinear Kirchhoff equation with non-homogeneous material (2014, background): “The case where M is the identity and V (x) = b > 0 is studied in [4] via minimization and in [13] by a monotonicity trick.”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, neutral): “For other results, we refer to [10,49].”
A multiplicity result for asymptotically linear Kirchhoff equations (2017, background): “1) in thewhole spaceRN (N ≥ 3), butwith thenonlinear term a(x)f(u)being replaced by a more general nonlinear term f(x, u), have also been studied extensively, see, for example, [8, 9, 12, 13, 15, 28, 35] and the references therein.”
Existence of a nodal solution with minimal energy for a Kirchhoff equation (2015, background): “Therefore, the study on this class of problems has increased considerably in the last ten years, as can be seen in [1], [2], [6], [10], [12]–[17], [19], [20]–[22], [26]–[29] and references therein.”
Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent (2013, neutral): “[11].”
Infinitely many sign-changing solutions for Kirchhoff type problems in R3 (2019, background): “See, for example, [13, 16, 35] and the references therein.”