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In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which concentrate at the minimum points of the potential $V$. Moreover, the monotonicity of $f(s)/s$ and the so-called Ambrosetti-Rabinowitz condition are not required.
In this paper, we study a class of Schr{o}dinger-Poisson (SP) systems with general nonlinearity where the nonlinearity does not require Ambrosetti-Rabinowitz and Nehari monotonic conditions. We establish new estimates and explore the associated energ
We investigate the existence of infinitely many radially symmetric solutions to the following problem $$(-Delta_p)^s u=g(u) textrm{ in } mathbb{R}^N, uin W^{s,p}(mathbb{R}^N),$$ where $sin (0,1)$, $2 leq p < infty$, $sp leq N $, $2 leq N in mat
In this paper, we consider the following Kirchhoff type equation $$ -left(a+ bint_{R^3}| abla u|^2right)triangle {u}+V(x)u=f(u),,,xinR^3, $$ where $a,b>0$ and $fin C(R,R)$, and the potential $Vin C^1(R^3,R)$ is positive, bounded and satisfies suitabl
In this paper, we study the long-time behavior of global solutions to the Schrodinger-Choquard equation $$ipartial_tu+Delta u=-(I_alphaast|cdot|^b|u|^{p})|cdot|^b|u|^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the non-ra
We study the inverse problem of recovery a non-linearity $f(x,u)$, which is compactly supported in $x$, in the semilinear wave equation $u_{tt}-Delta u+ f(x,u)=0$. We probe the medium with either complex or real-valued harmonic waves of wavelength $s