Nodal solutions for fractional elliptic equations involving exponential critical growth

Abstract

In the present paper, we study the existence of least energy nodal solution for a Dirichlet problem driven by the 12−Laplacian operator of the following type: false(−normalΔfalse)12u+Vfalse(xfalse)u=ffalse(ufalse)0.3em0.3emin0.3emfalse(a,bfalse),u=00.3em0.3emin.5emdouble-struckR∖false(a,bfalse), where V:false[a,bfalse]→false[0,+∞false) is a continuous potential and ffalse(tfalse) is a nonlinearity that grows like expfalse(t2false) as t→+∞. By using the constraint variational method and quantitative deformation lemma, we obtain a least energy nodal solution u for the given problem. Moreover, we show that the energy of u is strictly larger than twice the ground state energy.

Existence result for fractional problems with logarithmic and critical exponential nonlinearities

“…Since the fractional Trudinger-Moser inequality (see Lemma 2.1) was established, the existence and multiplicity of solutions for various nonlinear nonlocal problems with exponential nonlinearity were investigated. We refer to [1,2,6,9,10,12] and references therein.…”