One class of quasilinear elliptic type equations with discontinuous nonlinearities
V. N. Pavlenko, D. K. Potapov

References
1.	D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren Math. Wiss., 224, 2nd ed., Springer-Verlag, Berlin, 1983, xiii+513 pp.
2.	M. A. Krasnosel'skiĭ, A. V. Pokrovskiĭ, Systems with hysteresis, Springer-Verlag, Berlin, 1989, xviii+410 pp.
3.	H. J. Kuiper, “On positive solutions of nonlinear elliptic eigenvalue problems”, Rend. Circ. Mat. Palermo (2), 20:2-3 (1971), 113–138
4.	M. A. Krasnosel'skii, A. V. Pokrovskii, “Regular solutions of equations with discontinuous nonlinearities”, Soviet Math. Dokl., 17:1 (1976), 128–132
5.	V. N. Pavlenko, D. K. Potapov, “The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities”, Sb. Math., 206:9 (2015), 1281–1298
6.	V. N. Pavlenko, D. K. Potapov, “Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity”, Siberian Adv. Math., 27:1 (2017), 16–25
7.	V. N. Pavlenko, D. K. Potapov, “Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides”, Sb. Math., 208:1 (2017), 157–172
8.	V. N. Pavlenko, D. K. Potapov, “Existence of three nontrivial solutions of an elliptic boundary-value problem with discontinuous nonlinearity in the case of strong resonance”, Math. Notes, 101:2 (2017), 284–296
9.	V. N. Pavlenko, D. K. Potapov, “Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities”, Siberian Math. J., 58:2 (2017), 288–295
10.	V. N. Pavlenko, D. K. Potapov, “Elenbaas problem of electric arc discharge”, Math. Notes, 103:1 (2018), 89–95
11.	V. N. Pavlenko, D. K. Potapov, “Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity”, Sb. Math., 210:7 (2019), 1043–1066
12.	V. N. Pavlenko, D. K. Potapov, “On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity”, Izv. Math., 84:3 (2020), 592–607
13.	V. N. Pavlenko, D. K. Potapov, “On the existence of three nontrivial solutions of a resonance elliptic boundary value problem with a discontinuous nonlinearity”, Differ. Equ., 56:7 (2020), 831–841
14.	V. N. Pavlenko, D. K. Potapov, “Positive solutions of superlinear elliptic problems with discontinuous non-linearities”, Izv. Math., 85:2 (2021), 262–278
15.	V. N. Pavlenko, D. K. Potapov, “Variational method for elliptic systems with discontinuous nonlinearities”, Sb. Math., 212:5 (2021), 726–744
16.	V. N. Pavlenko, D. K. Potapov, “Existence of semiregular solutions of elliptic systems with discontinuous nonlinearities”, Math. Notes, 110:2 (2021), 226–241
17.	H. J. Kuiper, “Eigenvalue problems for noncontinuous operators associated with quasilinear elliptic equations”, Arch. Ration. Mech. Anal., 53:2 (1974), 178–186
18.	I. V. Shragin, “Conditions for measurability of superpositions”, Soviet Math. Dokl., 12 (1971), 465–470
19.	M. A. Krasnosel'skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964, 381 pp.
20.	Kung-ching Chang, “Free boundary problems and the set-valued mappings”, J. Differential Equations, 49:1 (1983), 1–28
21.	S. L. Sobolev, Some applications of functional analysis in mathematical physics, Transl. Math. Monogr., 90, Amer. Math. Soc., Providence, RI, 1991, viii+286 pp.
22.	O. A. Ladyzhenskaya, N. N. Ural'tseva, Linear and quasilinear elliptic equations, Academic Press, New York–London, 1968, xviii+495 pp.
23.	V. N. Pavlenko, “Control of singular distributed parabolic systems with discontinuous nonlinearities”, Ukrainian Math. J., 46:6 (1994), 790–798
24.	Yu. G. Borisovich, B. D. Gelman, A. D. Myshkis, V. V. Obukhovskii, Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, 2-e izd., ispr. i dop., Librokom, M., 2011, 224 pp.
25.	H. J. Kuiper, W. R. Derrick, “Nonlinear ordinary and functional Sturm–Liouville problems”, Indiana Univ. Math. J., 25:2 (1976), 179–190
26.	J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York–London–Paris, 1969, vii+236 pp.