This paper is devoted to introduce a new double phase elliptic inclusion problem (DPEI) involving nonlinear and nonhomogeneous partial differential operator which has unbalanced growth and logarithmic perturbation terms, and two multivalued functions which are defined in the domain and its boundary. The main goal of this paper is to establish the existence and extremality results to the elliptic inclusion problem under consideration. More exactly, we give the definitions of weak solutions, subsolutions and supersolutions to (DPEI). Then, under the coercive setting, an existence theorem of weak solutions to (DPEI) is obtained by employing a surjectivity theorem for pseudomonotone operators. Moreover, in the noncoercive framework, we apply the method of sub-supersolution combined with the nonsmooth calculus analysis and truncation techniques to prove that (DPEI) has at least a weak solution within an ordered interval of sub-supersolution. Finally, when the constraint set K satisfies a lattice condition, the existence of smallest and greatest elements of solution set to (DPEI) is established.

Liu, Y.J., Lu, Y.S., Vetro, C. (2024). A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 129 [10.1016/j.cnsns.2023.107683].

A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results

Vetro, C
2024-01-01

Abstract

This paper is devoted to introduce a new double phase elliptic inclusion problem (DPEI) involving nonlinear and nonhomogeneous partial differential operator which has unbalanced growth and logarithmic perturbation terms, and two multivalued functions which are defined in the domain and its boundary. The main goal of this paper is to establish the existence and extremality results to the elliptic inclusion problem under consideration. More exactly, we give the definitions of weak solutions, subsolutions and supersolutions to (DPEI). Then, under the coercive setting, an existence theorem of weak solutions to (DPEI) is obtained by employing a surjectivity theorem for pseudomonotone operators. Moreover, in the noncoercive framework, we apply the method of sub-supersolution combined with the nonsmooth calculus analysis and truncation techniques to prove that (DPEI) has at least a weak solution within an ordered interval of sub-supersolution. Finally, when the constraint set K satisfies a lattice condition, the existence of smallest and greatest elements of solution set to (DPEI) is established.
2024
Settore MAT/05 - Analisi Matematica
Liu, Y.J., Lu, Y.S., Vetro, C. (2024). A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 129 [10.1016/j.cnsns.2023.107683].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/621393
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