Using the variational principle of Ricceri and a local mountain pass lemma, we study the existence of three distinct solutions for the following resonant Duffing-type equations with damping and perturbed term, a.e., and without perturbed term, a.e.,.
Taking in Theorem 3.1, we can obtain the existence of three distinct solutions for the Duffing-type equation without perturbation (1.2) as following.
Then, there exists a constant ℓ̂ with the following property: for each compact interval ([a_{0},b_{0} ]subset( hat{ell}, +infty)), there exists a number (tau > 0) such that, for each (thetain[0,tau]), the problem (N) has at least three distinct solutions for every (lambdain[a_{0},b_{0} ]).
Due to Lemma 2.7 with (Gamma=lambda H ), we conclude that for each compact interval ([a_{0},b_{0} ]subset( hat{ell}, +infty)), there exists a number (tau > 0) such that, for each (thetain[0,tau]), the problem (N) has at least three distinct solutions for every (lambdain[a_{0},b_{0} ]).
SQL LIMS, for example, has distinct solutions for pharmaceutical laboratories, chemical, nourishing, forensic and water analysis laboratories.
This pressure apparently triggered independent evolution of several distinct solutions for the set of relatively simple reactions that are required for ROS detoxification.
CLUMPP v. 1.1.1 [ 26] was applied to avoid the potential effect of generating several distinct solutions for the estimated cluster membership coefficients in spite of identical initial conditions The average cluster membership was calculated using the LargeK Greedy algorithm.
In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices.
Therefore, there is a distinct need for solutions for the prevention and management of obesity and its related conditions.
