Nonexistence results for some nonlinear elliptic and parabolic inequalities with functional parameters

Nonexistence results for some nonlinear nonlocal elliptic inequalities with variable exponents

“…The purpose of this work is to study the nonexistence of nontrivial positive solutions to some classes of nonlinear elliptic inequalities involving the fractional diffusion operator (−Δ) α /2 ,0 < α < 2, and variable exponents. In order to obtain sufficient conditions for the nonexistence of solutions, we make use of the test function method introduced in , and developed in many recent works (see , and the references therein). Our motivation comes from the recent article of Galakhov et al , , where nonexistence results were obtained for some elliptic and parabolic inequalities with functional parameters involving the p ( x )‐Laplacian.…”

“…In order to obtain sufficient conditions for the nonexistence of solutions, we make use of the test function method introduced in , and developed in many recent works (see , and the references therein). Our motivation comes from the recent article of Galakhov et al , , where nonexistence results were obtained for some elliptic and parabolic inequalities with functional parameters involving the p ( x )‐Laplacian. First, we consider the elliptic inequality where , and .…”

“…/˛= 2 , 0 <˛< 2, and variable exponents. In order to obtain sufficient conditions for the nonexistence of solutions, we make use of the test function method introduced in [13], and developed in many recent works (see [5,8,[14][15][16][17][18][19][20][21], and the references therein). Our motivation comes from the recent article of Galakhov et al [16], where nonexistence results were obtained for some elliptic and parabolic inequalities with functional parameters involving the p.x/-Laplacian.…”