Abstract
In this paper, we prove the existence of bounded solutions of uni- lateral problems for strongly nonlinear equations whose principal part hav- ing a growth not necessarily of polynomial type and a degenerate coercivity, the lower order terms do not satisfy the sign condition and appropriate inte- grable source terms. We do not impose the �2-condition on the considered N-functions defining the Orlicz-Sobolev functional framework. Let be a bounded open subset of R N ; N � 2; and let M be an N-function. In this paper, we establish the existence of bounded solutions for the unilateral problem related to strongly nonlinear equations of the form
Highlights
Let Ω be a bounded open subset of RN, N ≥ 2, and let M be an N-function
We establish the existence of bounded solutions for the unilateral problem related to strongly nonlinear equations of the form
Tk(s) = max{−k, min{k, s}}, k > 0, is the truncation function defined on R
Summary
Let Ω be a bounded open subset of RN , N ≥ 2, and let M be an N-function. In this paper, we establish the existence of bounded solutions for the unilateral problem related to strongly nonlinear equations of the form. Tk(s) = max{−k, min{k, s}}, k > 0, is the truncation function defined on R It is our purpose, in this paper, to prove the existence of bounded solutions, for unilateral problem associated to (1.1) in the setting of the Orlicz-Sobolev spaces without assuming the ∆2-condition on the N-function M. In this paper, to prove the existence of bounded solutions, for unilateral problem associated to (1.1) in the setting of the Orlicz-Sobolev spaces without assuming the ∆2-condition on the N-function M To this end, we use rearrangement techniques and conditions (3.6) and (3.7), (see [18]), on the source term covering (1.6) in the case of polynomial growth.
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