Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities

The existence of multiple solutions for a class of fourth elliptic equation with respect to the resonance and nonresonance conditions is established by using the minimax method and Morse theory

Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality

Multiple solutions for a class of fractional equations

In this paper we study a class of fractional Laplace equations with asymptotically linear right-hand side. The existence results of three nontrivial solutions under the resonance and non-resonance conditions are established by using the minimax method and Morse theory