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In this paper, we study the existence of solutions for strongly nonlinear degenerated elliptic unilateral problems of the form \(A(u)+ g(x,u,\nabla u)+ H(x,\nabla u)=f\), where A is a Leray–Lions operator acting from \(W_0^{1,p}(\Omega ,w)\) to its dual. On the nonlinear term \(g(x,s,\xi )\), we assume growth condition on \(\xi \) and a sign condition on s, while the convection term \(H(x,\xi )\) is only growing at most as \(|\xi |^{p-1}\). The right-hand side f belongs to \(L^1(\Omega )\).

Titanium alloys have been widely used in industries, especially aerospace, energy and medical industries, due to their good mechanical and chemical properties. However, titanium alloys are typically difficult-to-cut materials. That is why, in industries we are using many process to cut this alloys. In fact, several studies have made a comparisons between the various machining processes currently used in industries to cut Titanium alloys.

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This open, randomised, cross-over study compared the acceptance and safety of NovoPen 3 with that of conventional syringes and vials when initiating insulin treatment in 96 NIDDM patients with secondary failure to oral hypoglycaemic agents. These patients had not previously been treated with insulin. All patients used each insulin administration system for 12 weeks. Group A started therapy using NovoPen 3 and crossed over to syringe/vial administration; Group B started with syringe/vial administration followed by NovoPen 3. In total, 78 patients completed the study. Most patients in Group A initially found the insulin injections very easy or easy and many of those who found injections easy at first found them very easy by the end of week 12. During the first period, patients in Group B found insulin administration more difficult than those in Group A. Injection pain was significantly lower with NovoPen 3 than with syringes and vials (P = 0.0018). Patients in Group B reported a significantly lower level of injection pain after the switch to using NovoPen 3 (P = 0.0003). Acceptance of insulin injections was significantly higher by patients using NovoPen 3 than by those using syringes and vials (P = 0.0059). Setting and drawing up the dose of insulin was also easier for patients using NovoPen 3 (P = 0.0490). At the end of the study, most patients (89.5% (68/76 replies)) said that they preferred NovoPen 3 to syringes and vials. Glycaemic control improved compared with baseline after starting insulin therapy, with no differences between Groups A and B, or between the two injection systems. The number of reported hypoglycaemic episodes was very low and was not significantly different between Groups A and B, or between the two administration systems. No treatment-related adverse events were reported. We conclude that use of NovoPen 3 provides better acceptance of insulin injection than use of conventional syringes and vials during initiation of insulin therapy in NIDDM patients with secondary failure to treatment with oral hypoglycaemic agents.