Existence and multiplicity of solutions for second order periodic systems with the p-Laplacian and a nonsmooth potential

Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian

“…18) which yields that |un | p(t) is bounded since ν < p − .We claim that un is bounded. If not, suppose that the sequence un is not bounded.…”

“…Periodic problems involving the scalar p-Laplacian were studied by many authors. We mention the works by Dang and Oppenheimer [10], Del Pino, Manasevich and Murua [11], Gasinski and Papageorgiou [16][17][18], Papageorgiou and Rǎdulescu [30], Yang [38] and the references [15,22,28,[30][31][32]38].…”

Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian

“…For the problems with a fractional Laplace operator, we refer to Liu and Tan [33], Liu et al [31], Migórski et al [35,38], Autuori and Pucci [1], Chen et al [9], Choi et al [12], Stinga and Torrea [44], Mosconi et al [39], Caffarelli et al [6], Chen et al [8]. On the other hand, for the problems dealing with multivalued terms modeled by Clarke's subdifferential we refer to the papers of Averna et al [2], Denkowski et al [13][14][15][16], Filippakis et al [18,19], Gasiński [20,21], Gasiński et al [22], Gasiński and Papageorgiou [24,25], Kalita and Kowalski [27], Papageorgiou et al [41,42], Zeng et al [48]. Finally, for the problems dealing with obstacle problems we refer to the papers of Caffarelli et al [4], Caffarelli et al [5], Choe [10], Choe and Lewis [11], Feehan and Pop [17], Oberman [40].…”