Nontrivial solutions of Kirchhoff-type problems via the Yang index

596 citations recorded by the source corpus.

Abstract We obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the Yang index and critical groups.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Multiplicity of solutions for a class of Kirchhoff type problems (2010, methodology): “Zhang [ 15 ] obtained a nontrivial solution of (1) by using the Yang index and critical group.”
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.”
Soliton solutions to Kirchhoff type problems involving the critical growth in RN (2013, background): “Some important and interesting results can be found; see for example [12–16].”
Multiplicity of high energy solutions for superlinear Kirchhoff equations (2012, background): “Perera and Zhang [11] proved the existence of one nontrivial solution to (1.”
Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity (2015, background): “on a smooth bounded domain Ω ⊂ R and f : Ω × R → R a continuous function, has been extensively studied(see[1],[3],[10],[11],[15]-[20],[22],[23],[30]).”