Nontrivial Solutions for Perturbations of the p-Laplacian on Unbounded Domains

Multiple solutions for a class of Kirchhoff type problems with concave nonlinearity

“…In the present paper, the following Proposition 1.1, variant Mountain Pass Theorem, which can been seen in [2] for the original version Mountain Pass Theorem, and Proposition 1.2 (Ekeland variational principle) are our main tools, which can be found in [9] and [16], respectively. Proposition 1.1.…”

Solutions to Semilinear Elliptic Problems with Combined Nonlinearities

“…In this section, we use a variant version of Mountain Pass Theorem to get a nonzero critical point of functional I; this theorem is used also in [11] and its proof can be found in [14,23], let us recall first this theorem. …”

The existence of infinitely many solutions for p-Laplacian type equations on R^N with linking geometry

“…The existence of a nontrivial solution to (1.4) can be obtained by using the mountain-pass theorem and the existence of infinitely many solutions, when g(x, t) is odd in t, can be obtained by the so-called fountain theorem, see e.g. [1,8,12,22,27,38].…”