Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior

Abstract

Existence and bifurcation of positive solutions to a Kirchhoff type equationare considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff type equation in bounded domain, and in our results the nonlinearity may be resonant near zero or infinity.

Study of a nonlinear Kirchhoff equation with non-homogeneous material

“…In [25] variational results were employed for nonlinearities f which are resonant at an eigenvalue. In [15] existence of positive solutions was showed using topological degree arguments and variational method for functions f asymptotically linear at zero and asymptotically 3-linear at infinity. When Ω = IR N the problem…”

Positive solutions of Kirchhoff type elliptic equations in with critical growth

“…The solvability of (1.1) is also discussed in mathematics [4], [10][11][12]. For the analysis of the stationary problems of (1.1), we refer the readers to [1], [2], [9], [15], [22], [28], [29], [31], [36], [37] and the references therein.…”

Existência E Multiplicidade De Soluções Para Uma Equação Elítica Quaselinear Do Tipo Kirchhoff

“…Eles obtiveram via métodos variacionais a existência de uma solução positiva, uma solução negativa e uma solução mudando de sinal para o problema (3). Por sua vez, Liang et al (2013) via o argumento do grau topológico e métodos variacionais obtiveram a existência de soluções positivas para o problema:…”