This paper discusses a class of nonlinear Schrödinger equations and presents a variational approach to proving existence results for these equations. The work is motivated by recent studies on nonlinear Schrödinger equations, particularly by Floer and Weinstein, who used a Lyapunov-Schmidt reduction to prove the existence of standing wave solutions. Oh later generalized these results and studied the stability of such solutions. However, the previous work assumed that the potential V belongs to a specific class of potentials (V)_a, which excludes rapidly oscillating potentials like sin(x²). The paper aims to show how variational methods, based on variants of the Mountain Pass Theorem, can be used to prove existence results for the equation complementary to those in previous works. It allows for a broader class of potentials, including highly oscillatory ones not in (V)_a. The paper also notes that the size of ħ is not important for the results, except in a specific theorem. The main equation considered is a semilinear elliptic PDE: -Δv + b(x)v = f(x, v), where b and f satisfy certain conditions. The paper provides hypotheses for b and f that will be used in the next section. These conditions include continuity, growth conditions, and a condition on the nonlinearity f. The paper concludes that the variational approach can be used to prove existence results for the equation, even for highly oscillatory potentials.This paper discusses a class of nonlinear Schrödinger equations and presents a variational approach to proving existence results for these equations. The work is motivated by recent studies on nonlinear Schrödinger equations, particularly by Floer and Weinstein, who used a Lyapunov-Schmidt reduction to prove the existence of standing wave solutions. Oh later generalized these results and studied the stability of such solutions. However, the previous work assumed that the potential V belongs to a specific class of potentials (V)_a, which excludes rapidly oscillating potentials like sin(x²). The paper aims to show how variational methods, based on variants of the Mountain Pass Theorem, can be used to prove existence results for the equation complementary to those in previous works. It allows for a broader class of potentials, including highly oscillatory ones not in (V)_a. The paper also notes that the size of ħ is not important for the results, except in a specific theorem. The main equation considered is a semilinear elliptic PDE: -Δv + b(x)v = f(x, v), where b and f satisfy certain conditions. The paper provides hypotheses for b and f that will be used in the next section. These conditions include continuity, growth conditions, and a condition on the nonlinearity f. The paper concludes that the variational approach can be used to prove existence results for the equation, even for highly oscillatory potentials.