Sentence examples for multiple nontrivial solutions from inspiring English sources

For this jumping nonlinearity, we are interested in the multiple nontrivial solutions of the equation.

We obtain multiple nontrivial solutions of (1) by proving the local (PS) condition and energy estimates.

In Section 5, we investigate the existence of multiple nontrivial solutions for perturbations of beam system (1.1).

Zhang and Li [7] proved the existence of multiple nontrivial solutions by means of Morse theory and local linking.

We investigate the existence of multiple nontrivial solutions for perturbations and of the beam system with Dirichlet boundary condition in, in, where, and are nonzero constants.

Let be the beam operator in, In this paper, we investigate the existence of multiple nontrivial solutions for perturbations of the beam system with Dirichlet boundary condition (1.1).

We will say that a certain property holds in ] α, β [ if it takes place on every closed subinterval of ] α, β [. Recall that we consider the problem (1), (2), where p, q ∈ L loc ( ] a, b [ ). Theorem 1.2 Let (3) hold. Then the homogeneous problem (1a), (2) has no more than one, up to a constant multiple, nontrivial solution.

By using a variety of fixed point theorems we begin with the establishment of the existence of a solution (not necessary positive) and proceed to the existence of a nontrivial positive solution, two nontrivial positive solutions, and multiple nontrivial positive solutions.

In this section, we establish criteria for the existence of one, two, or multiple nontrivial positive solutions of (1.1).

In [9], the existence of multiple nontrivial weak solutions for some parametric non-local equations with the nonlinear term having a sublinear growth at infinity is got via Variational methods.

Some existence and multiplicity results of nontrivial solutions are obtained.