Bound states of a nonhomogeneous nonlinear Schrödinger equation with non symmetric potential

Abstract

Bound state solutions are found via a linking theorem for a class of nonhomogeneous nonlinear Schrödinger equations with nonsymmetric potentials, using concentration compactness arguments and projections on a general Pohozaev type manifold.Mathematics Subject Classification. 35J20, 35J60, 35Q55.

Existence of bound state solutions for p-Laplacian equation with critical growth

“…We remark that (SQ) is essential to prove the existence of nontrivial solutions for (1.3) in all literature. Furthermore, other existence or multiplicity results can be found in [1,6,9,10,21,29,30] with variant assumptions on the nonlinearities.…”

Positive solutions for quasilinear Schrödinger equations in $\mathbb{R}^N$

“…In [22] it was assumed that h(x, u) is 1604 XIANG-DONG FANG differentiable with respect to x ∈ R N . They employed the minimization methods restricted to the Pohozaev manifold to obtain the existence of positive solutions for the asymptotically linear case (see also [23,27]). Later in [7] it extended the result given in [22] to more general quasilinear equations.…”

A positive solution for an asymptotically cubic quasilinear Schrödinger equation

“…In [10] and [16], for the non symmetric asymptotically linear case, they obtained a Mountain Pass positive solution. Later in [18], under restrictive conditions on the potential V , the existence of a 52 XIANG-DONG FANG positive solution corresponding to higher energy levels was shown, see also [17]. Subsequently, the result in [17] was extended to the quasilinear Schrödinger problem (see [5]).…”