Sign-changing solutions for some nonlinear problems with strong resonance

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Multiple Solutions and a Sign-Changing Solution for Semi-Linear Elliptic Problems with Resonance

Multiple Positive Solutions for Nonlinear Second-order M-point Boundary-value Problems with Sign Changing Nonlinearities

In this paper, we study the nonlinear second-order m-point boundary value problem u′′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, βu(0)− γu′(0) = 0, u(1) = m−2 X i=1 αiu(ξi), where the nonlinear term f is allowed to change sign. We impose growth conditions on f which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green’s function...

Existence results for equilibrium problems under strong sign property

This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of  upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some exist...

Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

and Applied Analysis 3 where a ∈ [0, π), b ∈ C([0, 1], [0, +∞)) and c, γ > 0. It is easy to verify that all conditions ofTheorem 4 are satisfied. So, BVP (1)with the nonlinear term (10) has at least two solutions, one positive and the other negative. Reference [7, Theorem 3.3] can only guarantee a nonzero solution for this example. Theorem 7. Assume that (H1)–(H5) hold. Then, BVP (1) has at lea...